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Cos pi/2

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

Cos pi/2: 0
Cos (-pi/2): 0
Cos pi/2 in degrees: cos (90°)

What is the Value of Cos pi/2?

The value of cos pi/2 is 0. Cos 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
∴ cos pi/2 = cos π/2 = cos(90°) = 0

Explanation:

For cos pi/2, the angle pi/2 lies on the positive y-axis. Thus, cos pi/2 value = 0
Since the cosine function is a periodic function, we can represent cos pi/2 as, cos pi/2 = cos(pi/2 + n × 2pi), n ∈ Z.
⇒ cos pi/2 = cos 5pi/2 = cos 9pi/2 , and so on.
Note: Since, cosine is an even function, the value of cos(-pi/2) = cos(pi/2) = 0.

Methods to Find Value of Cos pi/2

The value of cos pi/2 is given as 0. We can find the value of cos pi/2 by:

Using Trigonometric Functions
Using Unit Circle

Cos pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos pi/2 as:

± √(1-sin²(pi/2))
± 1/√(1 + tan²(pi/2))
± cot(pi/2)/√(1 + cot²(pi/2))
±√(cosec²(pi/2) - 1)/cosec(pi/2)
1/sec(pi/2)

Note: Since pi/2 lies on the positive y-axis, the final value of cos pi/2 is 0.

We can use trigonometric identities to represent cos pi/2 as,

-cos(pi - pi/2) = -cos pi/2
-cos(pi + pi/2) = -cos 3pi/2
sin(pi/2 + pi/2) = sin pi
sin(pi/2 - pi/2) = sin 0

Cos pi/2 Using Unit Circle

To find the value of cos π/2 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/2 angle with the positive x-axis.
The cos of pi/2 equals the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.

Hence the value of cos pi/2 = x = 0

☛ Also Check:

Examples Using Cos pi/2

Example 1: Find the value of 2 cos(pi/2)/3 sin(pi/2).

Solution:

Using trigonometric values, we know, cos(pi/2) = 0 and sin(pi/2) = 1.
⇒ Value of 2 cos(pi/2)/3 sin(pi/2) = 0
Example 2: Simplify: 8 (cos(pi/2)/cos(0))

Solution:

We know cos pi/2 = 0 and cos 0 = 1
⇒ 8 (cos(pi/2)/cos(0)) = 0
Example 3: Find the value of cos pi/2 if sin pi/2 is 1 and cot pi/2 = 0.

Solution:
Since, cot pi/2 = cos(pi/2)/sin(pi/2)
⇒ cos pi/2 = 0

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FAQs on Cos pi/2

What is Cos pi/2?

Cos pi/2 is the value of cosine trigonometric function for an angle equal to π/2 radians. The value of cos pi/2 is 0.

What is the Value of Cos pi/2 in Terms of Tan pi/2?

We know, using trig identities, we can write cos pi/2 as 1/√(1 + tan²(pi/2)).

How to Find Cos pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos pi/2 can be given in terms of other trigonometric functions as:

± √(1-sin²(pi/2))
± 1/√(1 + tan²(pi/2))
± cot(pi/2)/√(1 + cot²(pi/2))
±√(cosec²(pi/2) - 1)/cosec(pi/2)
1/sec(pi/2)

☛ Also check: trigonometry table

How to Find the Value of Cos pi/2?

The value of cos 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 cos pi/2 is equal to the x-coordinate (0). ∴ cos pi/2 = 0.

What is the Value of Cos pi/2 in Terms of Cosec pi/2?

Since the cosine function can be represented using the cosecant function, we can write cos pi/2 as [√(cosec²(pi/2) - 1)/cosec pi/2]. The value of cosec pi/2 is equal to 1.

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