Find Value Of Sin 3pi/2 - Cuemath

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 y-axis. 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 x-axis.
• The sin of 3pi/2 equals the y-coordinate(-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:

• ± √(1-cos²(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 y-axis, 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:

• tan 3pi/8
• cot 15pi/4
• cot pi/4
• tan 5pi/3
• cos pi/3
• sin 4pi/3