Cos 9pi/2

The value of cos 9pi/2 is 0. Cos 9pi/2 radians in degrees is written as cos ((9π/2) × 180°/π), i.e., cos (810°). In this article, we will discuss the methods to find the value of cos 9pi/2 with examples.

• Cos 9pi/2: 0
• Cos (-9pi/2): 0
• Cos 9pi/2 in degrees: cos (810°)

What is the Value of Cos 9pi/2?

The value of cos 9pi/2 is 0. Cos 9pi/2 can also be expressed using the equivalent of the given angle (9pi/2) in degrees (810°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 9pi/2 radians = 9pi/2 × (180°/pi) = 810° or 810 degrees
∴ cos 9pi/2 = cos 9π/2 = cos(810°) = 0

Explanation:

For cos 9pi/2, the angle 9pi/2 > 2pi. We can represent cos 9pi/2 as, cos(9pi/2 mod 2pi) = cos(pi/2). For cos 9pi/2, the angle 9pi/2 lies on the positive y-axis. Thus, cos 9pi/2 value = 0
Since the cosine function is a periodic function, we can represent cos 9pi/2 as, cos 9pi/2 = cos(9pi/2 + n × 2pi), n ∈ Z.
⇒ cos 9pi/2 = cos 13pi/2 = cos 17pi/2 , and so on.
Note: Since, cosine is an even function, the value of cos(-9pi/2) = cos(9pi/2) = 0.

Methods to Find Value of Cos 9pi/2

The value of cos 9pi/2 is given as 0. We can find the value of cos 9pi/2 by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 9pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 9pi/2 as:

• ± √(1-sin²(9pi/2))
• ± 1/√(1 + tan²(9pi/2))
• ± cot(9pi/2)/√(1 + cot²(9pi/2))
• ±√(cosec²(9pi/2) - 1)/cosec(9pi/2)
• 1/sec(9pi/2)

Note: Since 9pi/2 lies on the positive y-axis, the final value of cos 9pi/2 is 0.

We can use trigonometric identities to represent cos 9pi/2 as,

• -cos(pi - 9pi/2) = -cos(-7pi/2)
• -cos(pi + 9pi/2) = -cos 11pi/2
• sin(pi/2 + 9pi/2) = sin 5pi
• sin(pi/2 - 9pi/2) = sin(-4pi)

Cos 9pi/2 Using Unit Circle

To find the value of cos 9π/2 using the unit circle, represent 9pi/2 in the form (2 × 2pi) + pi/2 [∵ 9pi/2>2pi] ∵ cosine is a periodic function, cos 9pi/2 = cos pi/2.

• Rotate ‘r’ anticlockwise to form pi/2 or 9pi/2 angle with the positive x-axis.
• The cos of 9pi/2 equals the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.

Hence the value of cos 9pi/2 = x = 0

☛ Also Check:

• tan 5pi/6
• cos 4pi
• tan 11pi 6
• tan 7pi/3
• sin 11pi/6
• cos 7pi/6

FAQs on Cos 9pi/2

What is Cos 9pi/2?

Cos 9pi/2 is the value of cosine trigonometric function for an angle equal to 9π/2 radians. The value of cos 9pi/2 is 0.

How to Find Cos 9pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 9pi/2 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(9pi/2))
• ± 1/√(1 + tan²(9pi/2))
• ± cot(9pi/2)/√(1 + cot²(9pi/2))
• ±√(cosec²(9pi/2) - 1)/cosec(9pi/2)
• 1/sec(9pi/2)

☛ Also check: trigonometry table

What is the Value of Cos 9pi/2 in Terms of Sec 9pi/2?

Since the secant function is the reciprocal of the cosine function, we can write cos 9pi/2 as 1/sec(9pi/2). 

What is the Value of Cos 9pi/2 in Terms of Sin 9pi/2?

Using trigonometric identities, we can write cos 9pi/2 in terms of sin 9pi/2 as, cos(9pi/2) = √(1 - sin²(9pi/2)). 

How to Find the Value of Cos 9pi/2?

The value of cos 9pi/2 can be calculated by constructing an angle of 9π/2 radians with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cos 9pi/2 is equal to the x-coordinate (0). ∴ cos 9pi/2 = 0.