Sin 9pi/2
The value of sin 9pi/2 is 1. Sin 9pi/2 radians in degrees is written as sin ((9π/2) × 180°/π), i.e., sin (810°). In this article, we will discuss the methods to find the value of sin 9pi/2 with examples.
 Sin 9pi/2: 1
 Sin (9pi/2): 1
 Sin 9pi/2 in degrees: sin (810°)
What is the Value of Sin 9pi/2?
The value of sin 9pi/2 is 1. Sin 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
∴ sin 9pi/2 = sin 9π/2 = sin(810°) = 1
Explanation:
For sin 9pi/2, the angle 9pi/2 > 2pi. We can represent sin 9pi/2 as, sin(9pi/2 mod 2pi) = sin(pi/2). For sin 9pi/2, the angle 9pi/2 lies on the positive yaxis. Thus, sin 9pi/2 value = 1
Since the sine function is a periodic function, we can represent sin 9pi/2 as, sin 9pi/2 = sin(9pi/2 + n × 2pi), n ∈ Z.
⇒ sin 9pi/2 = sin 13pi/2 = sin 17pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(9pi/2) = sin(9pi/2).
Methods to Find Value of Sin 9pi/2
The value of sin 9pi/2 is given as 1. We can find the value of sin 9pi/2 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 9pi/2 Using Unit Circle
To find the value of sin 9π/2 using the unit circle, represent 9pi/2 in the form (2 × 2pi) + pi/2 [∵ 9pi/2>2pi] ∵ sine is a periodic function, sin 9pi/2 = sin pi/2.
 Rotate ‘r’ anticlockwise to form pi/2 or 9pi/2 angle with the positive xaxis.
 The sin of 9pi/2 equals the ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sin 9pi/2 = y = 1
Sin 9pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 9pi/2 as:
 ± √(1cos²(9pi/2))
 ± tan(9pi/2)/√(1 + tan²(9pi/2))
 ± 1/√(1 + cot²(9pi/2))
 ± √(sec²(9pi/2)  1)/sec(9pi/2)
 1/cosec(9pi/2)
Note: Since 9pi/2 lies on the positive yaxis, the final value of sin 9pi/2 is 1.
We can use trigonometric identities to represent sin 9pi/2 as,
 sin(pi  9pi/2) = sin(7pi/2)
 sin(pi + 9pi/2) = sin 11pi/2
 cos(pi/2  9pi/2) = cos(4pi)
 cos(pi/2 + 9pi/2) = cos 5pi
☛ Also Check:
Examples Using Sin 9pi/2

Example 1: Find the value of 2 × (sin(9pi/4) cos(9pi/4)). [Hint: Use sin 9pi/2 = 1]
Solution:
Using the sin 2a formula,
2 sin(9pi/4) cos(9pi/4) = sin(2 × 9pi/4) = sin 9pi/2
∵ sin 9pi/2 = 1
⇒ 2 × (sin(9pi/4) cos(9pi/4)) = 1 
Example 2: Find the value of sin(9pi/2) if cosec(9pi/2) is 1.
Solution:
Since, sin 9pi/2 = 1/csc(9pi/2)
⇒ sin 9pi/2 = 1/1 = 1 
Example 3: Find the value of 5 sin(9pi/2)/7 cos(4pi).
Solution:
Using trigonometric identities, we know, sin(9pi/2) = cos(pi/2  9pi/2) = cos(4pi).
⇒ sin(9pi/2) = cos(4pi)
⇒ Value of 5 sin(9pi/2)/7 cos(4pi) = 5/7
FAQs on Sin 9pi/2
What is Sin 9pi/2?
Sin 9pi/2 is the value of sine trigonometric function for an angle equal to 9pi/2 radians. The value of sin 9pi/2 is 1.
What is the Value of Sin 9pi/2 in Terms of Cos 9pi/2?
Using trigonometric identities, we can write sin 9pi/2 in terms of cos 9pi/2 as, sin(9pi/2) = √(1cos²(9pi/2)). Here, the value of cos 9pi/2 is equal to 0.
How to Find the Value of Sin 9pi/2?
The value of sin 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 sin 9pi/2 is equal to the ycoordinate (1). ∴ sin 9pi/2 = 1.
How to Find Sin 9pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 9π/2 can be given in terms of other trigonometric functions as:
 ± √(1cos²(9pi/2))
 ± tan(9pi/2)/√(1 + tan²(9pi/2))
 ± 1/√(1 + cot²(9pi/2))
 ± √(sec²(9pi/2)  1)/sec(9pi/2)
 1/cosec(9pi/2)
☛ Also check: trigonometric table
What is the Value of Sin 9pi/2 in Terms of Sec 9pi/2?
Since the sine function can be represented using the secant function, we can write sin 9pi/2 as √(sec²(9pi/2)  1)/sec 9pi/2.
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