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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 y-axis. 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:

± √(1-cos²(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 y-axis, 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 x-axis.
The sin of pi/2 equals the y-coordinate(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: (1-cos²(pi/2)).

Solution:
We know, (1-cos²(pi/2)) = (sin²(pi/2)) = 1
⇒ (1-cos²(pi/2)) = 1

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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 x-axis, 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 y-coordinate (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:

± √(1-cos²(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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