Cos 7pi/12
The value of cos 7pi/12 is -0.2588190. . .. Cos 7pi/12 radians in degrees is written as cos ((7π/12) × 180°/π), i.e., cos (105°). In this article, we will discuss the methods to find the value of cos 7pi/12 with examples.
- Cos 7pi/12: -(√6-√2)/4
- Cos 7pi/12 in decimal: -0.2588190. . .
- Cos (-7pi/12): -0.2588190. . . or -(√6-√2)/4
- Cos 7pi/12 in degrees: cos (105°)
What is the Value of Cos 7pi/12?
The value of cos 7pi/12 in decimal is -0.258819045. . .. Cos 7pi/12 can also be expressed using the equivalent of the given angle (7pi/12) in degrees (105°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/12 radians = 7pi/12 × (180°/pi) = 105° or 105 degrees
∴ cos 7pi/12 = cos 7π/12 = cos(105°) = -(√6-√2)/4 or -0.2588190. . .
Explanation:
For cos 7pi/12, the angle 7pi/12 lies between pi/2 and pi (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 7pi/12 value = -(√6-√2)/4 or -0.2588190. . .
Since the cosine function is a periodic function, we can represent cos 7pi/12 as, cos 7pi/12 = cos(7pi/12 + n × 2pi), n ∈ Z.
⇒ cos 7pi/12 = cos 31pi/12 = cos 55pi/12 , and so on.
Note: Since, cosine is an even function, the value of cos(-7pi/12) = cos(7pi/12).
Methods to Find Value of Cos 7pi/12
The cosine function is negative in the 2nd quadrant. The value of cos 7pi/12 is given as -0.25881. . .. We can find the value of cos 7pi/12 by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 7pi/12 Using Unit Circle
To find the value of cos 7π/12 using the unit circle:
- Rotate ‘r’ anticlockwise to form 7pi/12 angle with the positive x-axis.
- The cos of 7pi/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 7pi/12 = x = -0.2588 (approx)
Cos 7pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 7pi/12 as:
- ± √(1-sin²(7pi/12))
- ± 1/√(1 + tan²(7pi/12))
- ± cot(7pi/12)/√(1 + cot²(7pi/12))
- ±√(cosec²(7pi/12) - 1)/cosec(7pi/12)
- 1/sec(7pi/12)
Note: Since 7pi/12 lies in the 2nd Quadrant, the final value of cos 7pi/12 will be negative.
We can use trigonometric identities to represent cos 7pi/12 as,
- -cos(pi - 7pi/12) = -cos 5pi/12
- -cos(pi + 7pi/12) = -cos 19pi/12
- sin(pi/2 + 7pi/12) = sin 13pi/12
- sin(pi/2 - 7pi/12) = sin(-pi/12)
☛ Also Check:
FAQs on Cos 7pi/12
What is Cos 7pi/12?
Cos 7pi/12 is the value of cosine trigonometric function for an angle equal to 7π/12 radians. The value of cos 7pi/12 is -(√6-√2)/4 or -0.2588 (approx)
How to Find Cos 7pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 7pi/12 can be given in terms of other trigonometric functions as:
- ± √(1-sin²(7pi/12))
- ± 1/√(1 + tan²(7pi/12))
- ± cot(7pi/12)/√(1 + cot²(7pi/12))
- ±√(cosec²(7pi/12) - 1)/cosec(7pi/12)
- 1/sec(7pi/12)
☛ Also check: trigonometric table
What is the Value of Cos 7pi/12 in Terms of Cot 7pi/12?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 7pi/12 can be written as cot(7pi/12)/√(1 + cot²(7pi/12)). Here, the value of cot 7pi/12 is equal to -0.26794.
How to Find the Value of Cos 7pi/12?
The value of cos 7pi/12 can be calculated by constructing an angle of 7π/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 7pi/12 is equal to the x-coordinate (-0.2588). ∴ cos 7pi/12 = -0.2588.
What is the Value of Cos 7pi/12 in Terms of Sec 7pi/12?
Since the secant function is the reciprocal of the cosine function, we can write cos 7pi/12 as 1/sec(7pi/12). The value of sec 7pi/12 is equal to -3.863703.