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Sin 3pi/2
The value of sin 3pi/2 is 1. Sin 3pi/2 radians in degrees is written as sin ((3π/2) × 180°/π), i.e., sin (270°). In this article, we will discuss the methods to find the value of sin 3pi/2 with examples.
 Sin 3pi/2: 1
 Sin (3pi/2): 1
 Sin 3pi/2 in degrees: sin (270°)
What is the Value of Sin 3pi/2?
The value of sin 3pi/2 is 1. Sin 3pi/2 can also be expressed using the equivalent of the given angle (3pi/2) in degrees (270°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 3pi/2 radians = 3pi/2 × (180°/pi) = 270° or 270 degrees
∴ sin 3pi/2 = sin 3π/2 = sin(270°) = 1
Explanation:
For sin 3pi/2, the angle 3pi/2 lies on the negative yaxis. Thus, sin 3pi/2 value = 1
Since the sine function is a periodic function, we can represent sin 3pi/2 as, sin 3pi/2 = sin(3pi/2 + n × 2pi), n ∈ Z.
⇒ sin 3pi/2 = sin 7pi/2 = sin 11pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(3pi/2) = sin(3pi/2).
Methods to Find Value of Sin 3pi/2
The value of sin 3pi/2 is given as 1. We can find the value of sin 3pi/2 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 3pi/2 Using Unit Circle
To find the value of sin 3π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form 3pi/2 angle with the positive xaxis.
 The sin of 3pi/2 equals the ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sin 3pi/2 = y = 1
Sin 3pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 3pi/2 as:
 ± √(1cos²(3pi/2))
 ± tan(3pi/2)/√(1 + tan²(3pi/2))
 ± 1/√(1 + cot²(3pi/2))
 ± √(sec²(3pi/2)  1)/sec(3pi/2)
 1/cosec(3pi/2)
Note: Since 3pi/2 lies on the negative yaxis, the final value of sin 3pi/2 is 1.
We can use trigonometric identities to represent sin 3pi/2 as,
 sin(pi  3pi/2) = sin(pi/2)
 sin(pi + 3pi/2) = sin 5pi/2
 cos(pi/2  3pi/2) = cos(pi)
 cos(pi/2 + 3pi/2) = cos 2pi
☛ Also Check:
Examples Using Sin 3pi/2

Example 1: Find the value of 2 × (sin(3pi/4) cos(3pi/4)). [Hint: Use sin 3pi/2 = 1]
Solution:
Using the sin 2a formula,
2 sin(3pi/4) cos(3pi/4) = sin(2 × 3pi/4) = sin 3pi/2
∵ sin 3pi/2 = 1
⇒ 2 × (sin(3pi/4) cos(3pi/4)) = 1 
Example 2: Simplify: 2 (sin(3pi/2)/sin(7pi/2))
Solution:
We know sin 3pi/2 = sin 7pi/2
⇒ 2 sin(3pi/2)/sin(7pi/2) = 2(sin(3pi/2)/sin(3pi/2))
= 2(1) = 2 
Example 3: Using the value of sin 3pi/2, solve: (1cos²(3pi/2)).
Solution:
We know, (1cos²(3pi/2)) = (sin²(3pi/2)) = 1
⇒ (1cos²(3pi/2)) = 1
FAQs on Sin 3pi/2
What is Sin 3pi/2?
Sin 3pi/2 is the value of sine trigonometric function for an angle equal to 3pi/2 radians. The value of sin 3pi/2 is 1.
What is the Value of Sin 3pi/2 in Terms of Cos 3pi/2?
Using trigonometric identities, we can write sin 3pi/2 in terms of cos 3pi/2 as, sin(3pi/2) = √(1cos²(3pi/2)). Here, the value of cos 3pi/2 is equal to 0.
What is the Value of Sin 3pi/2 in Terms of Cosec 3pi/2?
Since the cosecant function is the reciprocal of the sine function, we can write sin 3pi/2 as 1/cosec(3pi/2). The value of cosec 3pi/2 is equal to 1.
How to Find the Value of Sin 3pi/2?
The value of sin 3pi/2 can be calculated by constructing an angle of 3π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 3pi/2 is equal to the ycoordinate (1). ∴ sin 3pi/2 = 1.
How to Find Sin 3pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 3π/2 can be given in terms of other trigonometric functions as:
 ± √(1cos²(3pi/2))
 ± tan(3pi/2)/√(1 + tan²(3pi/2))
 ± 1/√(1 + cot²(3pi/2))
 ± √(sec²(3pi/2)  1)/sec(3pi/2)
 1/cosec(3pi/2)
☛ Also check: trigonometric table
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