from a handpicked tutor in LIVE 1to1 classes
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:
 ± √(1sin²(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 xaxis.
 The cos of 13pi/12 equals the xcoordinate(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:
Examples Using Cos 13pi/12

Example 1: Using the value of cos 13pi/12, solve: (1sin²(13pi/12)).
Solution:
We know, (1sin²(13pi/12)) = (cos²(13pi/12)) = 0.933
⇒ (1sin²(13pi/12)) = 0.933 
Example 2: Find the value of 2 cos(13pi/12)/3 sin(7pi/12).
Solution:
Using trigonometric identities, we know, cos(13pi/12) = sin(pi/2  13pi/12) = sin(7pi/12).
⇒ cos(13pi/12) = sin(7pi/12)
⇒ Value of 2 cos(13pi/12)/3 sin(7pi/12) = 2/3 
Example 3: Simplify: 9 (cos(13pi/12)/sin(19pi/12))
Solution:
We know cos 13pi/12 = sin 19pi/12
⇒ 9 cos(13pi/12)/sin(19pi/12) = 9 (cos(13pi/12)/cos(13pi/12))
= 9(1) = 9
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:
 ± √(1sin²(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 xaxis, 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 xcoordinate (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.
visual curriculum