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 yaxis. 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:
 ± √(1sin²(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 yaxis, 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 xaxis.
 The cos of 9pi/2 equals the xcoordinate(0) of the point of intersection (0, 1) of unit circle and r.
Hence the value of cos 9pi/2 = x = 0
☛ Also Check:
Examples Using Cos 9pi/2

Example 1: Using the value of cos 9pi/2, solve: (1sin²(9pi/2)).
Solution:
We know, (1sin²(9pi/2)) = (cos²(9pi/2)) = 0
⇒ (1sin²(9pi/2)) = 0 
Example 2: Find the value of 2 cos(9pi/2)/3 sin(pi/2).
Solution:
Using trigonometric values, we know, cos(9pi/2) = 0 and sin(pi/2) = 1.
⇒ Value of 2 cos(9pi/2)/3 sin(pi/2) = 0 
Example 3: Find the value of cos 9pi/2 if sin 9pi/2 is 1 and cot 9pi/2 is 0.
Solution:
Since, cot 9pi/2 = cos(9pi/2)/sin(9pi/2)
⇒ cos 9pi/2 = 0
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:
 ± √(1sin²(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 xaxis, 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 xcoordinate (0). ∴ cos 9pi/2 = 0.