from a handpicked tutor in LIVE 1to1 classes
Sin 17pi/12
The value of sin 17pi/12 is 0.9659258. . .. Sin 17pi/12 radians in degrees is written as sin ((17π/12) × 180°/π), i.e., sin (255°). In this article, we will discuss the methods to find the value of sin 17pi/12 with examples.
 Sin 17pi/12: (√6 + √2)/4
 Sin 17pi/12 in decimal: 0.9659258. . .
 Sin (17pi/12): 0.9659258. . . or (√6 + √2)/4
 Sin 17pi/12 in degrees: sin (255°)
What is the Value of Sin 17pi/12?
The value of sin 17pi/12 in decimal is 0.965925826. . .. Sin 17pi/12 can also be expressed using the equivalent of the given angle (17pi/12) in degrees (255°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 17pi/12 radians = 17pi/12 × (180°/pi) = 255° or 255 degrees
∴ sin 17pi/12 = sin 17π/12 = sin(255°) = (√6 + √2)/4 or 0.9659258. . .
Explanation:
For sin 17pi/12, the angle 17pi/12 lies between pi and 3pi/2 (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 17pi/12 value = (√6 + √2)/4 or 0.9659258. . .
Since the sine function is a periodic function, we can represent sin 17pi/12 as, sin 17pi/12 = sin(17pi/12 + n × 2pi), n ∈ Z.
⇒ sin 17pi/12 = sin 41pi/12 = sin 65pi/12 , and so on.
Note: Since, sine is an odd function, the value of sin(17pi/12) = sin(17pi/12).
Methods to Find Value of Sin 17pi/12
The sine function is negative in the 3rd quadrant. The value of sin 17pi/12 is given as 0.96592. . .. We can find the value of sin 17pi/12 by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 17pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 17pi/12 as:
 ± √(1cos²(17pi/12))
 ± tan(17pi/12)/√(1 + tan²(17pi/12))
 ± 1/√(1 + cot²(17pi/12))
 ± √(sec²(17pi/12)  1)/sec(17pi/12)
 1/cosec(17pi/12)
Note: Since 17pi/12 lies in the 3rd Quadrant, the final value of sin 17pi/12 will be negative.
We can use trigonometric identities to represent sin 17pi/12 as,
 sin(pi  17pi/12) = sin(5pi/12)
 sin(pi + 17pi/12) = sin 29pi/12
 cos(pi/2  17pi/12) = cos(11pi/12)
 cos(pi/2 + 17pi/12) = cos 23pi/12
Sin 17pi/12 Using Unit Circle
To find the value of sin 17π/12 using the unit circle:
 Rotate ‘r’ anticlockwise to form 17pi/12 angle with the positive xaxis.
 The sin of 17pi/12 equals the ycoordinate(0.9659) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of sin 17pi/12 = y = 0.9659 (approx)
☛ Also Check:
Examples Using Sin 17pi/12

Example 1: Using the value of sin 17pi/12, solve: (1cos²(17pi/12)).
Solution:
We know, (1cos²(17pi/12)) = (sin²(17pi/12)) = 0.933
⇒ (1cos²(17pi/12)) = 0.933 
Example 2: Find the value of 5 sin(17pi/12)/7 cos(11pi/12).
Solution:
Using trigonometric identities, we know, sin(17pi/12) = cos(pi/2  17pi/12) = cos(11pi/12).
⇒ sin(17pi/12) = cos(11pi/12)
⇒ Value of 5 sin(17pi/12)/7 cos(11pi/12) = 5/7 
Example 3: Simplify: 3 (sin(17pi/12)/sin(41pi/12))
Solution:
We know sin 17pi/12 = sin 41pi/12
⇒ 3 sin(17pi/12)/sin(41pi/12) = 3(sin(17pi/12)/sin(17pi/12))
= 3(1) = 3
FAQs on Sin 17pi/12
What is Sin 17pi/12?
Sin 17pi/12 is the value of sine trigonometric function for an angle equal to 17pi/12 radians. The value of sin 17pi/12 is (√6 + √2)/4 or 0.9659 (approx).
What is the Value of Sin 17pi/12 in Terms of Sec 17pi/12?
Since the sine function can be represented using the secant function, we can write sin 17pi/12 as √(sec²(17pi/12)  1)/sec 17pi/12. The value of sec 17pi/12 is equal to 3.863703.
How to Find Sin 17pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 17π/12 can be given in terms of other trigonometric functions as:
 ± √(1cos²(17pi/12))
 ± tan(17pi/12)/√(1 + tan²(17pi/12))
 ± 1/√(1 + cot²(17pi/12))
 ± √(sec²(17pi/12)  1)/sec(17pi/12)
 1/cosec(17pi/12)
☛ Also check: trigonometric table
How to Find the Value of Sin 17pi/12?
The value of sin 17pi/12 can be calculated by constructing an angle of 17π/12 radians with the xaxis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of sin 17pi/12 is equal to the ycoordinate (0.9659). ∴ sin 17pi/12 = 0.9659.
What is the Value of Sin 17pi/12 in Terms of Cos 17pi/12?
Using trigonometric identities, we can write sin 17pi/12 in terms of cos 17pi/12 as, sin(17pi/12) = √(1cos²(17pi/12)). Here, the value of cos 17pi/12 is equal to (√6√2)/4.
visual curriculum