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

Cos 90 Degrees

The value of cos 90 degrees is 0. Cos 90 degrees in radians is written as cos (90° × π/180°), i.e., cos (π/2) or cos (1.570796. . .). In this article, we will discuss the methods to find the value of cos 90 degrees with examples.

Cos 90°: 0
Cos (-90 degrees): 0
Cos 90° in radians: cos (π/2) or cos (1.5707963 . . .)

What is the Value of Cos 90 Degrees?

The value of cos 90 degrees is 0. Cos 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 . . .
∴ cos 90° = cos(1.5707) = 0

Explanation:

For cos 90 degrees, the angle 90° lies on the positive y-axis. Thus cos 90° value = 0
Since the cosine function is a periodic function, we can represent cos 90° as, cos 90 degrees = cos(90° + n × 360°), n ∈ Z.
⇒ cos 90° = cos 450° = cos 810°, and so on.
Note: Since, cosine is an even function, the value of cos(-90°) = cos(90°) = 0.

Methods to Find Value of Cos 90 Degrees

The value of cos 90° is given as 0. We can find the value of cos 90 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cos 90° in Terms of Trigonometric Functions

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

± √(1-sin²(90°))
± 1/√(1 + tan²(90°))
± cot 90°/√(1 + cot²(90°))
±√(cosec²(90°) - 1)/cosec 90°
1/sec 90°

Note: Since 90° lies on the positive y-axis, the final value of cos 90° will be 0.

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

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

Cos 90 Degrees Using Unit Circle

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

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

Hence the value of cos 90° = x = 0

☛ Also Check:

Examples Using Cos 90 Degrees

Example 1: Simplify: 5 (cos 90°/sin 90°)

Solution:

We know cos 90° = 0 and sin 90° = 1
⇒ 5 cos 90°/sin 90° = 5 (0)
= 0
Example 2: Find the value of 2 cos(90°)/3 cos(0°).

Solution:

Using trigonometric identities, we know, cos(90°) = 0 and cos 0° = 1.
⇒ Value of 2 cos(90°)/3 cos(0°) = 0
Example 3: Using the value of cos 90°, solve: (1-sin²(90°)).

Solution:
We know, (1-sin²(90°)) = (cos²(90°)) = 0
⇒ (1-sin²(90°)) = 0

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 Cos 90 Degrees

What is Cos 90 Degrees?

Cos 90 degrees is the value of cosine trigonometric function for an angle equal to 90 degrees. The value of cos 90° is 0.

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

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

± √(1-sin²(90°))
± 1/√(1 + tan²(90°))
± cot 90°/√(1 + cot²(90°))
± √(cosec²(90°) - 1)/cosec 90°
1/sec 90°

☛ Also check: trigonometric table

What is the Value of Cos 90° in Terms of Cosec 90°?

Since the cosine function can be represented using the cosecant function, we can write cos 90° as [√(cosec²(90°) - 1)/cosec 90°]. The value of cosec 90° is equal to 1.

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

Using trigonometric identities, we can write cos 90° in terms of sin 90° as, cos(90°) = √(1 - sin²(90°)). Here, the value of sin 90° is equal to 1.

How to Find the Value of Cos 90 Degrees?

The value of cos 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 cos 90° is equal to the x-coordinate (0). ∴ cos 90° = 0.

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum