Cos 5pi/12

The value of cos 5pi/12 is 0.2588190. . .. Cos 5pi/12 radians in degrees is written as cos ((5π/12) × 180°/π), i.e., cos (75°). In this article, we will discuss the methods to find the value of cos 5pi/12 with examples.

• Cos 5pi/12: (√6 - √2)/4
• Cos 5pi/12 in decimal: 0.2588190. . .
• Cos (-5pi/12): 0.2588190. . . or (√6-√2)/4
• Cos 5pi/12 in degrees: cos (75°)

What is the Value of Cos 5pi/12?

The value of cos 5pi/12 in decimal is 0.258819045. . .. Cos 5pi/12 can also be expressed using the equivalent of the given angle (5pi/12) in degrees (75°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/12 radians = 5pi/12 × (180°/pi) = 75° or 75 degrees
∴ cos 5pi/12 = cos 5π/12 = cos(75°) = (√6 - √2)/4 or 0.2588190. . .

Explanation:

For cos 5pi/12, the angle 5pi/12 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 5pi/12 value = (√6 - √2)/4 or 0.2588190. . .
Since the cosine function is a periodic function, we can represent cos 5pi/12 as, cos 5pi/12 = cos(5pi/12 + n × 2pi), n ∈ Z.
⇒ cos 5pi/12 = cos 29pi/12 = cos 53pi/12 , and so on.
Note: Since, cosine is an even function, the value of cos(-5pi/12) = cos(5pi/12).

Methods to Find Value of Cos 5pi/12

The cosine function is positive in the 1st quadrant. The value of cos 5pi/12 is given as 0.25881. . .. We can find the value of cos 5pi/12 by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 5pi/12 Using Unit Circle

To find the value of cos 5π/12 using the unit circle:

• Rotate ‘r’ anticlockwise to form 5pi/12 angle with the positive x-axis.
• The cos of 5pi/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 5pi/12 = x = 0.2588 (approx)

Cos 5pi/12 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 5pi/12 as:

• ± √(1-sin²(5pi/12))
• ± 1/√(1 + tan²(5pi/12))
• ± cot(5pi/12)/√(1 + cot²(5pi/12))
• ±√(cosec²(5pi/12) - 1)/cosec(5pi/12)
• 1/sec(5pi/12)

Note: Since 5pi/12 lies in the 1st Quadrant, the final value of cos 5pi/12 will be positive.

We can use trigonometric identities to represent cos 5pi/12 as,

• -cos(pi - 5pi/12) = -cos 7pi/12
• -cos(pi + 5pi/12) = -cos 17pi/12
• sin(pi/2 + 5pi/12) = sin 11pi/12
• sin(pi/2 - 5pi/12) = sin pi/12

☛ Also Check:

• cot 15pi/4
• tan 2pi
• sin 5pi/8
• cos 4pi
• sec pi/3
• cot 2pi

FAQs on Cos 5pi/12

What is Cos 5pi/12?

Cos 5pi/12 is the value of cosine trigonometric function for an angle equal to 5π/12 radians. The value of cos 5pi/12 is (√6 - √2)/4 or 0.2588 (approx)

What is the Exact Value of cos 5pi/12?

The exact value of cos 5pi/12 can be given accurately up to 8 decimal places as 0.25881904 and (√6 - √2)/4 in fraction.

What is the Value of Cos 5pi/12 in Terms of Tan 5pi/12?

We know, using trig identities, we can write cos 5pi/12 as 1/√(1 + tan²(5pi/12)). Here, the value of tan 5pi/12 is equal to 3.732050.

How to Find the Value of Cos 5pi/12?

The value of cos 5pi/12 can be calculated by constructing an angle of 5π/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 5pi/12 is equal to the x-coordinate (0.2588). ∴ cos 5pi/12 = 0.2588.

How to Find Cos 5pi/12 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 5pi/12 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(5pi/12))
• ± 1/√(1 + tan²(5pi/12))
• ± cot(5pi/12)/√(1 + cot²(5pi/12))
• ±√(cosec²(5pi/12) - 1)/cosec(5pi/12)
• 1/sec(5pi/12)

☛ Also check: trigonometry table