Sin pi/2
The value of sin pi/2 is 1. Sin pi/2 radians in degrees is written as sin ((π/2) × 180°/π), i.e., sin (90°). In this article, we will discuss the methods to find the value of sin pi/2 with examples.
 Sin pi/2: 1
 Sin (pi/2): 1
 Sin pi/2 in degrees: sin (90°)
What is the Value of Sin pi/2?
The value of sin pi/2 is 1. Sin pi/2 can also be expressed using the equivalent of the given angle (pi/2) in degrees (90°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/2 radians = pi/2 × (180°/pi) = 90° or 90 degrees
∴ sin pi/2 = sin π/2 = sin(90°) = 1
Explanation:
For sin pi/2, the angle pi/2 lies on the positive yaxis. Thus, sin pi/2 value = 1
Since the sine function is a periodic function, we can represent sin pi/2 as, sin pi/2 = sin(pi/2 + n × 2pi), n ∈ Z.
⇒ sin pi/2 = sin 5pi/2 = sin 9pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(pi/2) = sin(pi/2).
Methods to Find Value of Sin pi/2
The value of sin pi/2 is given as 1. We can find the value of sin pi/2 by:
 Using Trigonometric Functions
 Using Unit Circle
Sin pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin pi/2 as:
 ± √(1cos²(pi/2))
 ± tan(pi/2)/√(1 + tan²(pi/2))
 ± 1/√(1 + cot²(pi/2))
 ± √(sec²(pi/2)  1)/sec(pi/2)
 1/cosec(pi/2)
Note: Since pi/2 lies on the positive yaxis, the final value of sin pi/2 is 1.
We can use trigonometric identities to represent sin pi/2 as,
 sin(pi  pi/2) = sin pi/2
 sin(pi + pi/2) = sin 3pi/2
 cos(pi/2  pi/2) = cos 0
 cos(pi/2 + pi/2) = cos pi
Sin pi/2 Using Unit Circle
To find the value of sin π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/2 angle with the positive xaxis.
 The sin of pi/2 equals the ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sin pi/2 = y = 1
☛ Also Check:
Examples Using Sin pi/2

Example 1: Find the value of sin(pi/2) if cosec(pi/2) is 1.
Solution:
Since, sin pi/2 = 1/csc(pi/2)
⇒ sin pi/2 = 1/1 = 1 
Example 2: Find the value of 5 sin(pi/2)/7 cos(0).
Solution:
Using trigonometric identities, we know, sin(pi/2) = cos(pi/2  pi/2) = cos(0).
⇒ sin(pi/2) = cos(0)
⇒ Value of 5 sin(pi/2)/7 cos(0) = 5/7 
Example 3: Using the value of sin pi/2, solve: (1cos²(pi/2)).
Solution:
We know, (1cos²(pi/2)) = (sin²(pi/2)) = 1
⇒ (1cos²(pi/2)) = 1
FAQs on Sin pi/2
What is Sin pi/2?
Sin pi/2 is the value of sine trigonometric function for an angle equal to pi/2 radians. The value of sin pi/2 is 1.
What is the Value of Sin pi/2 in Terms of Cot pi/2?
We can represent the sine function in terms of the cotangent function using trig identities, sin pi/2 can be written as 1/√(1 + cot²(pi/2)). Here, the value of cot pi/2 is equal to 0.
How to Find the Value of Sin pi/2?
The value of sin pi/2 can be calculated by constructing an angle of π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin pi/2 is equal to the ycoordinate (1). ∴ sin pi/2 = 1.
What is the Value of Sin pi/2 in Terms of Cosec pi/2?
Since the cosecant function is the reciprocal of the sine function, we can write sin pi/2 as 1/cosec(pi/2). The value of cosec pi/2 is equal to 1.
How to Find Sin pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin π/2 can be given in terms of other trigonometric functions as:
 ± √(1cos²(pi/2))
 ± tan(pi/2)/√(1 + tan²(pi/2))
 ± 1/√(1 + cot²(pi/2))
 ± √(sec²(pi/2)  1)/sec(pi/2)
 1/cosec(pi/2)
☛ Also check: trigonometric table
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