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:

• ± √(1-cos²(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 x-axis.
• The sin of 17pi/12 equals the y-coordinate(-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:

• cos 11pi/12
• cos 7pi/12
• cot 4pi/3
• sin pi/4
• cos 13pi/12
• cos 5pi/4

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:

• ± √(1-cos²(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 x-axis, 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 y-coordinate (-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) = -√(1-cos²(17pi/12)). Here, the value of cos 17pi/12 is equal to -(√6-√2)/4.