Sin 150 degrees in fraction

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Sin 150 degrees in fraction. To find the value of tan 150 degrees using the unit circle: Rotate ‘r’ anticlockwise to form 150° angle with the positive x-axis. The tan of 150 degrees equals the y-coordinate (0.5) divided by x-coordinate (-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r. Hence the value of tan 150° = y/x = -0.5774 (approx).

For sin 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant ). Since sine function is positive in the first quadrant, thus sin 15° value = (√6 - √2)/4 or 0.2588190. . . Since the sine function is a periodic function, we can represent sin 15° as, sin 15 degrees = sin (15° + n × 360°), n ∈ Z. ⇒ sin 15° = sin 375 ...

Step 1: Compute the exact value of cos 150 °: Since, 150 ° = 180 °-30 ° So we can write cos 150 ° as. cos 150 ° = cos 180 °-30 ° =-cos 30 ° ∵ cos (180-θ) =-cos θ =-3 2 ∵ cos 30 ° = 3 2. Step 2: Compute the exact value of sin 150 °: We can find the value as. sin 150 ° = sin 180 °-30 ° = sin 30 ° ∵ sin 180-θ = sin θ = 1 2 ... The value of tan 30 degrees in decimal is 0.577350269.... The tangent of 30 degrees can be found by taking the sine of 30 degrees and dividing it by the cosine of 30 degrees. Since the sine of 30 degrees is 1/2 and the cosine of 30 degrees is √3/2, the tangent of 30 degrees is. tan 30° = (sin 30°)/ (cos 30°) = (1/2) / (√3/2) = 1/√3.Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepThe value of Sin 150° is ½. The steps involved in the calculation are sin (150°) = sin (180 – 30)° = sin 30° = ½. The explanation of these steps has been provided in the following. We find that the value of sin of 150 degrees and the value of sin of 30 degrees are equal. The angle of 150 degrees lies within the 2 nd quadrant. Hence, we ...Although the Bible does clearly show that people need to repent for all sins, there is no passage that says that all sins are equal; instead, the Bible shows some sins cause more g... Evaluate sin(150) Step 1. Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Step 2. The exact value of is . Step 3. a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 180°/π ~ 57.3 degrees. secant. the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos (θ) sin. sin (θ) is the ratio of the opposite side of angle θ ...

Order of Operations Factors & Primes Fractions Long Arithmetic Decimals ... To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians ... sin 150. en ...Find the Exact Value sin (150) sin(150) sin ( 150) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. sin(30) sin ( 30) The exact value of … Popular Problems. Trigonometry. Find the Exact Value sin (150) sin(150) sin ( 150) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. sin(30) sin ( 30) The exact value of sin(30) sin ( 30) is 1 2 1 2. 1 2 1 2. The result can be shown in multiple forms. Exact Form: 1 2 1 2. Decimal Form: 0.5 0.5. Trigonometry. Evaluate sin (315 degrees ) sin(315°) sin ( 315 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant. −sin(45) - sin ( 45) The exact value of sin(45) sin ( 45) is √2 2 2 2. − √2 2 - 2 2.Answer: sin (150°) = 0.5. sin (150°) is exactly: 1/2. Note: angle unit is set to …

A tangent of an angle α is also equal to the ratio between its sine and cosine, so tanα = sinα / cosα. Following from the definition, the function results in an undefined value at certain angles, like 90°, ... Our tangent calculator accepts input in degrees or radians, so assuming the angle is known, ... 150 ° 5π/6-0.577350: 180 ...Sin 330 degrees is the value of sine trigonometric function for an angle equal to 330 degrees. ... Sin 330° in fraction:-(1/2) Sin (-330 degrees): 0.5; Sin 330° in radians: sin (11π/6) ... We can use trigonometric identities to represent sin 330° as, sin(180° - … Answer: tan (150°) = -0.5773502692. tan (150°) is exactly: -√3/3. Note: angle unit is set to degrees. Use our tan (x) calculator to find the exact value of tangent of 150 degrees as a fraction - tan (150 °) - or the tangent of any angle in degrees and in radians. Many brokerages will allow you to buy and sell fractional shares in exchange-traded funds, which can be a handy way to invest if you don't have much money available to put into the...

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The value of cos 300 degrees in decimal is 0.5. Cos 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .) ⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . . Explanation: For cos 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant ).Step 1: Compute the exact value of cos 150 °: Since, 150 ° = 180 ° - 30 °. So we can write cos 150 ° as. cos 150 ° = cos 180 ° - 30 ° = - cos 30 ° ∵ cos ( 180 - θ) = - cos θ. = - 3 2 …Calculate the value of sin 150 °: First, determine the sign of sin 150 °. It is clear that 150 ° belongs to the second quadrant. It is known that the values of sines are positive + in the second quadrant. It is also known that, sin (180-x) ° = sin x °. Thus, sin 150 ° = sin 180-30 ° = sin 30 ° = 1 2. Therefore, the value of sin 150 ...As the y coordinate is 0.5, sin 30° = 0.5. Why is sine 150 degrees equal to sin 30 degrees? 150° = 180°-30° So sine 150 degress is equal to sine 30 degrees because 150 degrees is in the second quadrant where sine is positive and the related angle is 30 degrees. Equivalent values of sin 30. These are some other values which sine 30 can be ...Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

The US government is set today to officially label Boko Haram, a Nigerian Islamist group, a ”foreign terrorist organization.” That means authorities would have the power to block f... Answer: sin (120°) = 0.8660254038. sin (120°) is exactly: √3/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 120 degrees - sin (120 °) - or the sine of any angle in degrees and in radians. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Step 1: Compute the exact value of cos 150 °: Since, 150 ° = 180 ° - 30 °. So we can write cos 150 ° as. cos 150 ° = cos 180 ° - 30 ° = - cos 30 ° ∵ cos ( 180 - θ) = - cos θ. = - 3 2 …To find the value of sin 10 degrees using the unit circle: Rotate ‘r’ anticlockwise to form a 10° angle with the positive x-axis. The sin of 10 degrees equals the y-coordinate (0.1736) of the point of intersection (0.9848, 0.1736) of unit circle and r. Hence the value of sin 10° = y = 0.1736 (approx)Answer: sin (135°) = 0.7071067812. sin (135°) is exactly: √2/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 135 degrees - sin (135 °) - or the sine of any angle in degrees and in radians.To find the value of cos 135 degrees using the unit circle: Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis. The cos of 135 degrees equals the x-coordinate (-0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r. Hence the value of cos 135° = x = -0.7071 (approx)Popular Problems. Precalculus. Find the Value Using the Unit Circle 150 degrees. 150° 150 °. Evaluate cos(150°) cos ( 150 °). Tap for more steps... − √3 2 - 3 2. Evaluate sin(150°) sin ( 150 °). Tap for more steps...Jan 2, 2024 · Thus, from solving a problem in three different ways and also by a few example problems, we were able to find the value of sin(150°) which turned out to be 0.5 or 1/2 in fraction form. Confession is an important sacrament in many religious traditions, offering believers the opportunity to reflect on their actions and seek forgiveness. One crucial aspect of confes...

First of all, observe that 150 = 180 −30. Then, remember that we have. Plug in x = 30 to get. the answer comes from the fact that cos(30) = √3 2 and sin(30) = 1 2 are known values. cos (150) = -sqrt (3)/2 sin (150) = 1/2 First of all, observe that 150=180-30. Then, remember that we have cos (180-x) = -cos (x) sin (180-x) = sin (x) Plug in x ...

Free math problem solver answers your trigonometry homework questions with step-by-step explanations.Calculate cos(150) cos is found using Adjacent/Hypotenuse. Determine quadrant: Since 90 150 180 degrees it is located in Quadrant II. sin is positive. Determine angle type: 150 > 90°, so it is obtuse. cos(150) = -√ 3 /2. Excel or Google Sheets formula: Excel or Google Sheets formula:=COS(RADIANS(150)) Special Angle Valuescot (150°) cot ( 150 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cotangent is negative in the second quadrant. −cot(30) - cot ( 30) The exact value of cot(30) cot ( 30) is √3 3. −√3 - 3.Trigonometry. Find the Exact Value sin (630) sin(630) sin ( 630) Remove full rotations of 360 360 ° until the angle is between 0 0 ° and 360 360 °. sin(270) sin ( 270) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.Duolingo is launching its math app, for adults and children, to the public today. It is available on iOS and is free for users. Duolingo is launching its math app to the public mon...Find the Exact Value sin (135 degrees ) sin(135°) sin ( 135 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. sin(45) sin ( 45) The exact value of sin(45) sin ( 45) is √2 2 2 2. √2 2 2 2. The result can be shown in multiple forms. Exact Form: √2 2 2 2.Trigonometry. Find the Exact Value sin (630) sin(630) sin ( 630) Remove full rotations of 360 360 ° until the angle is between 0 0 ° and 360 360 °. sin(270) sin ( 270) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.As the y coordinate is 0.5, sin 30° = 0.5. Why is sine 150 degrees equal to sin 30 degrees? 150° = 180°-30° So sine 150 degress is equal to sine 30 degrees because 150 degrees is in the second quadrant where sine is positive and the related angle is 30 degrees. Equivalent values of sin 30. These are some other values which sine 30 can be ...\sin (x)+\sin (\frac{x}{2})=0,\:0\le \:x\le \:2\pi \cos (x)-\sin (x)=0 \sin (4\theta)-\frac{\sqrt{3}}{2}=0,\:\forall 0\le\theta<2\pi ; 2\sin ^2(x)+3=7\sin (x),\:x\in[0,\:2\pi ] 3\tan …

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sin(225) sin ( 225) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant. −sin(45) - sin ( 45) The exact value of sin(45) sin ( 45) is √2 2 2 2. − √2 2 - 2 2. The result can be shown in multiple forms.Find the Exact Value sin(300) Step 1. Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant. Step 2. The exact value of is . Step 3. The result can be shown in multiple forms.Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical ...The integral of sin^2 is one-half of x, minus one-eighth of the sine of 4x, plus a constant. Using mathematical notation, the integral of sine squared can be written as sin^2 x dx ...Free math problem solver answers your trigonometry homework questions with step-by-step explanations.Decimal Form: - 0.5. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step …Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.Algebra. Fraction Calculator. Step 1: Enter the fraction you want to simplify. The Fraction Calculator will reduce a fraction to its simplest form. You can also add, subtract, multiply, and divide fractions, as well as, convert to a decimal and work with mixed numbers and reciprocals. We also offer step by step solutions.Step 1: Compute the exact value of cos 150 °: Since, 150 ° = 180 ° - 30 °. So we can write cos 150 ° as. cos 150 ° = cos 180 ° - 30 ° = - cos 30 ° ∵ cos ( 180 - θ) = - cos θ. = - 3 2 … From the above equations, we get sin 60 degrees exact value as √3/2. In the same way, we can find the values for cos and tan ratios. Therefore, the exact value of sin 60 degrees is √3/2. Cos 0° = Sin 90° = 1. Cos 30°= Sin 60° = √3/2. Cos 45° = Sin 45° = 1/√2. Cos 60° = Sin 30° =1/2. Answer: sin (330°) = -0.5. sin (330°) is exactly: -1/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 330 degrees - sin (330 °) - or the sine of any angle in degrees and in radians. ….

If you’ve been tapped to speak at the wedding reception, do not commit one of these faux pas. An estimated 2.5 million weddings are expected to take place this year in the United S...InvestorPlace - Stock Market News, Stock Advice & Trading Tips Environmental, social, governance (ESG) investing has been a major theme in rec... InvestorPlace - Stock Market N...sin(A – B) = [sin(A).cos(B)] – [cos(A).sin(B)] How do I find the value of sin 150° in fraction form? Solution: Method 1: sin(150°) We can write 150° as 180° – 30° So, …The value of cos 300 degrees in decimal is 0.5. Cos 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .) ⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . . Explanation: For cos 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant ).Answer: sin (60°) = 0.8660254038. sin (60°) is exactly: √3/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 60 degrees - sin (60 °) - or the sine of any angle in degrees and in radians.InvestorPlace - Stock Market News, Stock Advice & Trading Tips Environmental, social, governance (ESG) investing has been a major theme in rec... InvestorPlace - Stock Market N... sin(250) sin ( 250) The result can be shown in multiple forms. Exact Form: sin(250) sin ( 250) Decimal Form: −0.93969262… - 0.93969262 …. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. sin150° = 0.5. sin 150° = 0.5. sin 150 degrees = 0.5. The sin of 150 degrees is 0.5, the same as sin of 150 degrees in radians. To obtain 150 degrees in radian multiply 150° by π / 180° = 5/6 π. Sin 150degrees = sin (5/6 × π). Our results of sin150° have been rounded to five decimal places. If you want sine 150° with higher accuracy ...For sin 90 degrees, the angle 90° lies on the positive y-axis. Thus, sin 90° value = 1. Since the sine function is a periodic function, we can represent sin 90° as, sin 90 degrees = sin (90° + n × 360°), n ∈ Z. ⇒ sin 90° = sin 450° = sin 810°, and so on. Note: Since, sine is an odd function, the value of sin (-90°) = -sin (90°). Sin 150 degrees in fraction, The tan of 150 degrees is -√ (3)/3, the same as tan of 150 degrees in radians. To obtain 150 degrees in radian multiply 150° by π / 180° = 5/6 π. Tan 150degrees = tan (5/6 × π). Our results of tan150° have been rounded to five decimal places. If you want tangent 150° with higher accuracy, then use the calculator below; our tool ..., Explanation: For sin 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant ). Since sine function is positive in the first quadrant, thus sin 30° value = 1/2 or 0.5. Since the sine function is a periodic function, we can represent sin 30° as, sin 30 degrees = sin (30° + n × 360°), n ∈ Z. ⇒ sin 30° = sin 390° = sin 750 ..., Answer: sin (-150°) = -0.5. sin (-150°) is exactly: -1/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of -150 degrees - sin (-150 °) - or the sine of any angle in degrees and in radians., Answer: sin (150°) = 0.5. sin (150°) is exactly: 1/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 150 degrees - sin (150 °) - or the sine of any angle in degrees and in radians., Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ..., Explanation: sin( − 150∘) = − sin(150∘) = − sin(180∘ −30∘) = − sin(30∘) ( ∵ sin(180∘ − θ) = sinθ) = − 1 2. Answer link. Jacobi J. Jul 21, 2018. − 1 2. Explanation: …, The value of Sin 150° is ½. The steps involved in the calculation are sin (150°) = sin (180 – 30)° = sin 30° = ½. The explanation of these steps has been provided in the following. We find that the value of sin of 150 degrees and the value of sin of 30 degrees are equal. The angle of 150 degrees lies within the 2 nd quadrant. Hence, we ..., Confession is an important sacrament in many religious traditions, offering believers the opportunity to reflect on their actions and seek forgiveness. One crucial aspect of confes..., Related Queries: {sin(180 deg), sin(150 deg), sin(120 deg), sin(90 deg), sin(60 deg), sin(45 deg), sin(30 deg)} sin(pi/2), sin(pi/3), sin(pi/4), sin(pi/3), sin(pi/5 ..., Investors may want to turn toward these sin stocks as they offer high dividend yields and resistance against recessions. These sin stocks are undervalued and offer high yields Sour..., Order of Operations Factors & Primes Fractions Long Arithmetic Decimals ... To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians ... sin 150. en ..., Solution. Calculate the value of sin 150 °: First, determine the sign of sin 150 °. It is clear that 150 ° belongs to the second quadrant. It is known that the values of sines are positive + in the second quadrant. It is also known that, sin ( 180 - x) ° = sin x °. Thus, sin 150 ° = sin 180 - 30 ° = sin 30 ° = 1 2. , For sin 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant ). Since sine function is negative in the third quadrant, thus sin 210° value = - (1/2) or -0.5. Since the sine function is a periodic function, we can represent sin 210° as, sin 210 degrees = sin (210° + n × 360°), n ∈ Z. ⇒ sin 210° = sin 570° = sin ..., In this video, we learn to find the value of sin150. Here I have applied sin(180 - x) = sin(x) identity to find the value of sin(150). The URL of the video e..., 150° lies in the 2nd Quadrant. Therefore sin (180° – θ) = sin θ. sin (150°) = sin (180° – 30°) sin (150°) = sin (30°) sin (150°) = 1/2 So the exact value of sin 150° is 1/2. Similar Questions. Question 1: Find the value of sin 135°. Solution: Since, we know that sin is positive in the 1st and 2nd Quadrant,, Step 1: Compute the exact value of cos 150 °: Since, 150 ° = 180 ° - 30 °. So we can write cos 150 ° as. cos 150 ° = cos 180 ° - 30 ° = - cos 30 ° ∵ cos ( 180 - θ) = - cos θ. = - 3 2 …, Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ..., sin(A – B) = [sin(A).cos(B)] – [cos(A).sin(B)] How do I find the value of sin 150° in fraction form? Solution: Method 1: sin(150°) We can write 150° as 180° – 30° So, …, 15° 15 °. To convert degrees to radians, multiply by π 180° π 180 °, since a full circle is 360° 360 ° or 2π 2 π radians. 15°⋅ π 180° 15 ° ⋅ π 180 ° radians. Cancel the common factor of 15 15. Tap for more steps... π 12 π 12 radians., Trigonometry. Find the Exact Value sin (630) sin(630) sin ( 630) Remove full rotations of 360 360 ° until the angle is between 0 0 ° and 360 360 °. sin(270) sin ( 270) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant. , : Get the latest SIN CARS INDUSTRY AD Registered Shs stock price and detailed information including news, historical charts and realtime prices. Indices Commodities Currencies Sto..., To find the value of cos 135 degrees using the unit circle: Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis. The cos of 135 degrees equals the x-coordinate (-0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r. Hence the value of cos 135° = x = -0.7071 (approx), Answer: sin (120°) = 0.8660254038. sin (120°) is exactly: √3/2. Note: angle unit is set to degrees. Use our sin (x) calculator to find the exact value of sine of 120 degrees - sin (120 °) - or the sine of any angle in degrees and in radians. , Explanation: For sin 90 degrees, the angle 90° lies on the positive y-axis. Thus, sin 90° value = 1. Since the sine function is a periodic function, we can represent sin 90° as, sin 90 degrees = sin (90° + n × 360°), n ∈ Z. ⇒ sin 90° = sin 450° = sin 810°, and so on. Note: Since, sine is an odd function, the value of sin (-90 ..., Take the inverse identity of your decimal, e.g., sin⁻¹(0.5). The resulting number is the degree of your angle. Check your results with our trigonometry calculators., Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios ... degrees-to-radians-calculator. sin 150. en. Related Symbolab ..., My Delano Las Vegas review goes over all of the ins and outs of one of the most underrated properties in sin city. A great Amex FHR option. Increased Offer! Hilton No Annual Fee 70..., \sin (x)+\sin (\frac{x}{2})=0,\:0\le \:x\le \:2\pi \cos (x)-\sin (x)=0 \sin (4\theta)-\frac{\sqrt{3}}{2}=0,\:\forall 0\le\theta<2\pi ; 2\sin ^2(x)+3=7\sin (x),\:x\in[0,\:2\pi ] 3\tan …, Trigonometry. Find the Exact Value sin (240 degrees ) sin(240°) sin ( 240 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant. −sin(60) - sin ( 60), sin(250) sin ( 250) The result can be shown in multiple forms. Exact Form: sin(250) sin ( 250) Decimal Form: −0.93969262… - 0.93969262 …. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor., a unit of plane angular measurement that is equal to the angle at the center of a circle subtended by an arc whose length equals the radius or approximately 180°/π ~ 57.3 degrees. secant. the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos (θ) sin. sin (θ) is the ratio of the opposite side of angle θ ..., The sine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the opposite side to the longest side of the triangle. In the illustration below, sin(α) = a/c and sin(β) = b/c. From cos(α) = a/c follows that the sine of any angle is always less than or equal to ..., If we divide the numerator of the value of sin 15 in fractional form with its denominator we will get a decimal number. Let’s see how we can do that step by step. Value of sin 15 in fraction form = √3 – 1 2√2. We will substitute the values of √3 and √2 in the above fraction. We know that √3 = 1.732 and √2 = 1.414.