Find Value Of Cos 7pi/12 | Cos 7π/12 - Cuemath

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:

• cot 15pi/4
• sin 7pi
• cos 2pi/7
• sin 7pi/12
• cot pi/3
• cot pi/2