Cos 13pi/12

The value of cos 13pi/12 is -0.9659258. . .. Cos 13pi/12 radians in degrees is written as cos ((13π/12) × 180°/π), i.e., cos (195°). In this article, we will discuss the methods to find the value of cos 13pi/12 with examples.

• Cos 13pi/12: -(√6+√2)/4
• Cos 13pi/12 in decimal: -0.9659258. . .
• Cos (-13pi/12): -0.9659258. . . or -(√6+√2)/4
• Cos 13pi/12 in degrees: cos (195°)

What is the Value of Cos 13pi/12?

The value of cos 13pi/12 in decimal is -0.965925826. . .. Cos 13pi/12 can also be expressed using the equivalent of the given angle (13pi/12) in degrees (195°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 13pi/12 radians = 13pi/12 × (180°/pi) = 195° or 195 degrees
∴ cos 13pi/12 = cos 13π/12 = cos(195°) = -(√6+√2)/4 or -0.9659258. . .

Explanation:

For cos 13pi/12, the angle 13pi/12 lies between pi and 3pi/2 (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 13pi/12 value = -(√6+√2)/4 or -0.9659258. . .
Since the cosine function is a periodic function, we can represent cos 13pi/12 as, cos 13pi/12 = cos(13pi/12 + n × 2pi), n ∈ Z.
⇒ cos 13pi/12 = cos 37pi/12 = cos 61pi/12 , and so on.
Note: Since, cosine is an even function, the value of cos(-13pi/12) = cos(13pi/12).

Methods to Find Value of Cos 13pi/12

The cosine function is negative in the 3rd quadrant. The value of cos 13pi/12 is given as -0.96592. . .. We can find the value of cos 13pi/12 by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 13pi/12 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 13pi/12 as:

• ± √(1-sin²(13pi/12))
• ± 1/√(1 + tan²(13pi/12))
• ± cot(13pi/12)/√(1 + cot²(13pi/12))
• ±√(cosec²(13pi/12) - 1)/cosec(13pi/12)
• 1/sec(13pi/12)

Note: Since 13pi/12 lies in the 3rd Quadrant, the final value of cos 13pi/12 will be negative.

We can use trigonometric identities to represent cos 13pi/12 as,

• -cos(pi - 13pi/12) = -cos(-pi/12)
• -cos(pi + 13pi/12) = -cos 25pi/12
• sin(pi/2 + 13pi/12) = sin 19pi/12
• sin(pi/2 - 13pi/12) = sin(-7pi/12)

Cos 13pi/12 Using Unit Circle

To find the value of cos 13π/12 using the unit circle:

• Rotate ‘r’ anticlockwise to form 13pi/12 angle with the positive x-axis.
• The cos of 13pi/12 equals the x-coordinate(-0.9659) of the point of intersection (-0.9659, -0.2588) of unit circle and r.

Hence the value of cos 13pi/12 = x = -0.9659 (approx)

☛ Also Check:

• cos 2pi/8
• sin pi/2
• sin 5pi/12
• tan pi/2
• tan 2pi
• csc pi/4

FAQs on Cos 13pi/12

What is Cos 13pi/12?

Cos 13pi/12 is the value of cosine trigonometric function for an angle equal to 13π/12 radians. The value of cos 13pi/12 is -(√6+√2)/4 or -0.9659 (approx)

How to Find Cos 13pi/12 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 13pi/12 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(13pi/12))
• ± 1/√(1 + tan²(13pi/12))
• ± cot(13pi/12)/√(1 + cot²(13pi/12))
• ±√(cosec²(13pi/12) - 1)/cosec(13pi/12)
• 1/sec(13pi/12)

☛ Also check: trigonometric table

What is the Value of Cos 13pi/12 in Terms of Tan 13pi/12?

We know, using trig identities, we can write cos 13pi/12 as -1/√(1 + tan²(13pi/12)). Here, the value of tan 13pi/12 is equal to 0.267949.

How to Find the Value of Cos 13pi/12?

The value of cos 13pi/12 can be calculated by constructing an angle of 13π/12 radians with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, -0.2588) on the unit circle. The value of cos 13pi/12 is equal to the x-coordinate (-0.9659). ∴ cos 13pi/12 = -0.9659.

What is the Value of Cos 13pi/12 in Terms of Cosec 13pi/12?

Since the cosine function can be represented using the cosecant function, we can write cos 13pi/12 as [√(cosec²(13pi/12) - 1)/cosec 13pi/12]. The value of cosec 13pi/12 is equal to -3.86370.