A day full of math games & activities. Find one near you.

Sin 90 Degrees

The value of sin 90 degrees is 1. Sin 90 degrees in radians is written as sin (90° × π/180°), i.e., sin (π/2) or sin (1.570796. . .). In this article, we will discuss the methods to find the value of sin 90 degrees with examples.

Sin 90°: 1
Sin (-90 degrees): -1
Sin 90° in radians: sin (π/2) or sin (1.5707963 . . .)

What is the Value of Sin 90 Degrees?

The value of sin 90 degrees is 1. Sin 90 degrees can also be expressed using the equivalent of the given angle (90 degrees) in radians (1.57079 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 90 degrees = 90° × (π/180°) rad = π/2 or 1.5707 . . .
∴ sin 90° = sin(1.5707) = 1

Explanation:

For sin 90 degrees, the angle 90° lies on the positive y-axis. Thus, sin 90° value = 1
Since the sine function is a periodic function, we can represent sin 90° as, sin 90 degrees = sin(90° + n × 360°), n ∈ Z.
⇒ sin 90° = sin 450° = sin 810°, and so on.
Note: Since, sine is an odd function, the value of sin(-90°) = -sin(90°).

Methods to Find Value of Sin 90 Degrees

The value of sin 90° is given as 1. We can find the value of sin 90 degrees by:

Using Trigonometric Functions
Using Unit Circle

Sin 90° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 90 degrees as:

± √(1-cos²(90°))
± tan 90°/√(1 + tan²(90°))
± 1/√(1 + cot²(90°))
± √(sec²(90°) - 1)/sec 90°
1/cosec 90°

Note: Since 90° lies on the positive y-axis, the final value of sin 90° will be positive.

We can use trigonometric identities to represent sin 90° as,

sin(180° - 90°) = sin 90°
-sin(180° + 90°) = -sin 270°
cos(90° - 90°) = cos 0°
-cos(90° + 90°) = -cos 180°

Sin 90 Degrees Using Unit Circle

To find the value of sin 90 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.
The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 90° = y = 1.

☛ Also Check:

Examples Using Sin 90 Degrees

Example 1: Using the value of sin 90°, solve: (1-cos²(90°)).

Solution:
We know, (1-cos²(90°)) = (sin²(90°)) = 1
⇒ (1-cos²(90°)) = 1
Example 2: Simplify: 2 (sin 90°/sin 450°)

Solution:

We know sin 90° = sin 450°
⇒ 2 sin 90°/sin 450° = 2(sin 90°/sin 90°)
= 2(1) = 2
Example 3: Find the value of sin 90° if cosec 90° is 1.

Solution:
Since, sin 90° = 1/csc 90°
⇒ sin 90° = 1/1 = 1

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Sin 90 Degrees

What is Sin 90 Degrees?

Sin 90 degrees is the value of sine trigonometric function for an angle equal to 90 degrees. The value of sin 90° is 1.

How to Find the Value of Sin 90 Degrees?

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

How to Find Sin 90° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 90° can be given in terms of other trigonometric functions as:

± √(1-cos²(90°))
± tan 90°/√(1 + tan²(90°))
± 1/√(1 + cot²(90°))
± √(sec²(90°) - 1)/sec 90°
1/cosec 90°

☛ Also check: trigonometric table

What is the Exact Value of sin 90 Degrees?

The exact value of sin 90 degrees is 1.

What is the Value of Sin 90 Degrees in Terms of Cos 90°?

Using trigonometric identities, we can write sin 90° in terms of cos 90° as, sin(90°) = √(1-cos²(90°)). Here, the value of cos 90° is equal to 0.

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum