Cos 13pi/6
The value of cos 13pi/6 is 0.8660254. . .. Cos 13pi/6 radians in degrees is written as cos ((13π/6) × 180°/π), i.e., cos (390°). In this article, we will discuss the methods to find the value of cos 13pi/6 with examples.
- Cos 13pi/6: √3/2
- Cos 13pi/6 in decimal: 0.8660254. . .
- Cos (-13pi/6): 0.8660254. . . or √3/2
- Cos 13pi/6 in degrees: cos (390°)
What is the Value of Cos 13pi/6?
The value of cos 13pi/6 in decimal is 0.866025403. . .. Cos 13pi/6 can also be expressed using the equivalent of the given angle (13pi/6) in degrees (390°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 13pi/6 radians = 13pi/6 × (180°/pi) = 390° or 390 degrees
∴ cos 13pi/6 = cos 13π/6 = cos(390°) = √3/2 or 0.8660254. . .
Explanation:
For cos 13pi/6, the angle 13pi/6 > 2pi. Given the periodic property of the cosine function, we can represent it as cos(13pi/6 mod 2pi) = cos(pi/6). The angle 13pi/6, coterminal to angle pi/6, is located in the First Quadrant(Quadrant I).
Since cos function is positive in the 1st quadrant, thus cos 13pi/6 value = √3/2 or 0.8660254. . .
Similarly, cos 13pi/6 can also be written as, cos 13pi/6 = (13pi/6 + n × 2pi), n ∈ Z.
⇒ cos 13pi/6 = cos 25pi/6 = cos 37pi/6, and so on.
Note: Since, cosine is an even function, the value of cos(-13pi/6) = cos(13pi/6).
Methods to Find Value of Cos 13pi/6
The cosine function is positive in the 1st quadrant. The value of cos 13pi/6 is given as 0.86602. . .. We can find the value of cos 13pi/6 by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 13pi/6 Using Unit Circle
To find the value of cos 13π/6 using the unit circle, represent 13pi/6 in the form (1 × 2pi) + pi/6 [∵ 13pi/6>2pi] ∵ cosine is a periodic function, cos 13pi/6 = cos pi/6.
- Rotate ‘r’ anticlockwise to form pi/6 or 13pi/6 angle with the positive x-axis.
- The cos of 13pi/6 equals the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cos 13pi/6 = x = 0.866 (approx)
Cos 13pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 13pi/6 as:
- ± √(1-sin²(13pi/6))
- ± 1/√(1 + tan²(13pi/6))
- ± cot(13pi/6)/√(1 + cot²(13pi/6))
- ±√(cosec²(13pi/6) - 1)/cosec(13pi/6)
- 1/sec(13pi/6)
Note: Since 13pi/6 lies in the 1st Quadrant, the final value of cos 13pi/6 will be positive.
We can use trigonometric identities to represent cos 13pi/6 as,
- -cos(pi - 13pi/6) = -cos(-7pi/6)
- -cos(pi + 13pi/6) = -cos 19pi/6
- sin(pi/2 + 13pi/6) = sin 8pi/3
- sin(pi/2 - 13pi/6) = sin(-5pi/3)
☛ Also Check:
FAQs on Cos 13pi/6
What is Cos 13pi/6?
Cos 13pi/6 is the value of cosine trigonometric function for an angle equal to 13π/6 radians. The value of cos 13pi/6 is √3/2 or 0.866 (approx)
What is the Value of Cos 13pi/6 in Terms of Sec 13pi/6?
Since the secant function is the reciprocal of the cosine function, we can write cos 13pi/6 as 1/sec(13pi/6). The value of sec 13pi/6 is equal to 1.154700.
How to Find the Value of Cos 13pi/6?
The value of cos 13pi/6 can be calculated by constructing an angle of 13π/6 radians with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos 13pi/6 is equal to the x-coordinate (0.866). ∴ cos 13pi/6 = 0.866.
What is the Value of Cos 13pi/6 in Terms of Cot 13pi/6?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 13pi/6 can be written as cot(13pi/6)/√(1 + cot²(13pi/6)). Here, the value of cot 13pi/6 is equal to 1.73205.
How to Find Cos 13pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 13pi/6 can be given in terms of other trigonometric functions as:
- ± √(1-sin²(13pi/6))
- ± 1/√(1 + tan²(13pi/6))
- ± cot(13pi/6)/√(1 + cot²(13pi/6))
- ±√(cosec²(13pi/6) - 1)/cosec(13pi/6)
- 1/sec(13pi/6)
☛ Also check: trigonometry table