Cos 17pi/12

The value of cos 17pi/12 is -0.2588190. . .. Cos 17pi/12 radians in degrees is written as cos ((17π/12) × 180°/π), i.e., cos (255°). In this article, we will discuss the methods to find the value of cos 17pi/12 with examples.

• Cos 17pi/12: -(√6-√2)/4
• Cos 17pi/12 in decimal: -0.2588190. . .
• Cos (-17pi/12): -0.2588190. . . or -(√6-√2)/4
• Cos 17pi/12 in degrees: cos (255°)

What is the Value of Cos 17pi/12?

The value of cos 17pi/12 in decimal is -0.258819045. . .. Cos 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
∴ cos 17pi/12 = cos 17π/12 = cos(255°) = -(√6-√2)/4 or -0.2588190. . .

Explanation:

For cos 17pi/12, the angle 17pi/12 lies between pi and 3pi/2 (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 17pi/12 value = -(√6-√2)/4 or -0.2588190. . .
Since the cosine function is a periodic function, we can represent cos 17pi/12 as, cos 17pi/12 = cos(17pi/12 + n × 2pi), n ∈ Z.
⇒ cos 17pi/12 = cos 41pi/12 = cos 65pi/12 , and so on.
Note: Since, cosine is an even function, the value of cos(-17pi/12) = cos(17pi/12).

Methods to Find Value of Cos 17pi/12

The cosine function is negative in the 3rd quadrant. The value of cos 17pi/12 is given as -0.25881. . .. We can find the value of cos 17pi/12 by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 17pi/12 Using Unit Circle

To find the value of cos 17π/12 using the unit circle:

• Rotate ‘r’ anticlockwise to form 17pi/12 angle with the positive x-axis.
• The cos of 17pi/12 equals the x-coordinate(-0.2588) of the point of intersection (-0.2588, -0.9659) of unit circle and r.

Hence the value of cos 17pi/12 = x = -0.2588 (approx)

Cos 17pi/12 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 17pi/12 as:

• ± √(1-sin²(17pi/12))
• ± 1/√(1 + tan²(17pi/12))
• ± cot(17pi/12)/√(1 + cot²(17pi/12))
• ±√(cosec²(17pi/12) - 1)/cosec(17pi/12)
• 1/sec(17pi/12)

Note: Since 17pi/12 lies in the 3rd Quadrant, the final value of cos 17pi/12 will be negative.

We can use trigonometric identities to represent cos 17pi/12 as,

• -cos(pi - 17pi/12) = -cos(-5pi/12)
• -cos(pi + 17pi/12) = -cos 29pi/12
• sin(pi/2 + 17pi/12) = sin 23pi/12
• sin(pi/2 - 17pi/12) = sin(-11pi/12)

☛ Also Check:

• sec pi/2
• sec pi/3
• cos 9pi/2
• cos 3pi/8
• cot pi/2
• cos 11pi/12

FAQs on Cos 17pi/12

What is Cos 17pi/12?

Cos 17pi/12 is the value of cosine trigonometric function for an angle equal to 17π/12 radians. The value of cos 17pi/12 is -(√6-√2)/4 or -0.2588 (approx)

What is the Value of Cos 17pi/12 in Terms of Cosec 17pi/12?

Since the cosine function can be represented using the cosecant function, we can write cos 17pi/12 as [√(cosec²(17pi/12) - 1)/cosec 17pi/12]. The value of cosec 17pi/12 is equal to -1.03527.

How to Find the Value of Cos 17pi/12?

The value of cos 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 cos 17pi/12 is equal to the x-coordinate (-0.2588). ∴ cos 17pi/12 = -0.2588.

How to Find Cos 17pi/12 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 17pi/12 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(17pi/12))
• ± 1/√(1 + tan²(17pi/12))
• ± cot(17pi/12)/√(1 + cot²(17pi/12))
• ±√(cosec²(17pi/12) - 1)/cosec(17pi/12)
• 1/sec(17pi/12)

☛ Also check: trigonometric table

What is the Value of Cos 17pi/12 in Terms of Tan 17pi/12?

We know, using trig identities, we can write cos 17pi/12 as -1/√(1 + tan²(17pi/12)). Here, the value of tan 17pi/12 is equal to 3.732050.