Find Value Of Sin Pi/2 - Cuemath

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:

• tan pi
• cos 11pi/6
• tan 11pi/12
• cos 2pi/8
• sin 4pi/3
• cos 7pi/6