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Cos 3pi/2

The value of cos 3pi/2 is 0. Cos 3pi/2 radians in degrees is written as cos ((3π/2) × 180°/π), i.e., cos (270°). In this article, we will discuss the methods to find the value of cos 3pi/2 with examples.

Cos 3pi/2: 0
Cos (-3pi/2): 0
Cos 3pi/2 in degrees: cos (270°)

What is the Value of Cos 3pi/2?

The value of cos 3pi/2 is 0. Cos 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
∴ cos 3pi/2 = cos 3π/2 = cos(270°) = 0

Explanation:

For cos 3pi/2, the angle 3pi/2 lies on the negative y-axis. Thus, cos 3pi/2 value = 0
Since the cosine function is a periodic function, we can represent cos 3pi/2 as, cos 3pi/2 = cos(3pi/2 + n × 2pi), n ∈ Z.
⇒ cos 3pi/2 = cos 7pi/2 = cos 11pi/2 , and so on.
Note: Since, cosine is an even function, the value of cos(-3pi/2) = cos(3pi/2) = 0.

Methods to Find Value of Cos 3pi/2

The value of cos 3pi/2 is given as 0. We can find the value of cos 3pi/2 by:

Using Unit Circle
Using Trigonometric Functions

Cos 3pi/2 Using Unit Circle

To find the value of cos 3π/2 using the unit circle:

Rotate ‘r’ anticlockwise to form 3pi/2 angle with the positive x-axis.
The cos of 3pi/2 equals the x-coordinate(0) of the point of intersection (0, -1) of unit circle and r.

Hence the value of cos 3pi/2 = x = 0

Cos 3pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 3pi/2 as:

± √(1-sin²(3pi/2))
± 1/√(1 + tan²(3pi/2))
± cot(3pi/2)/√(1 + cot²(3pi/2))
±√(cosec²(3pi/2) - 1)/cosec(3pi/2)
1/sec(3pi/2)

Note: Since 3pi/2 lies on the negative y-axis, the final value of cos 3pi/2 is 0.

We can use trigonometric identities to represent cos 3pi/2 as,

-cos(pi - 3pi/2) = -cos(-pi/2)
-cos(pi + 3pi/2) = -cos 5pi/2
sin(pi/2 + 3pi/2) = sin 2pi
sin(pi/2 - 3pi/2) = sin(-pi)

☛ Also Check:

Examples Using Cos 3pi/2

Example 1: Using the value of cos 3pi/2, solve: (1-sin²(3pi/2)).

Solution:
We know, (1-sin²(3pi/2)) = (cos²(3pi/2)) = 0
⇒ (1-sin²(3pi/2)) = 0
Example 2: Find the value of 2 cos(3pi/2)/3 sin(pi/2).

Solution:

Using trigonometric values, we know, cos(3pi/2) = 0 and sin(pi/2) = 1.
⇒ Value of 2 cos(3pi/2)/3 sin(pi/2) = 0
Example 3: Find the value of cos 3pi/2 if sin 3pi/2 is -1 and cot 3pi/2 is 0.

Solution:
Since, cot 3pi/2 = cos (3pi/2)/sin(3pi/2)
⇒ cos 3pi/2 = 0

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FAQs on Cos 3pi/2

What is Cos 3pi/2?

Cos 3pi/2 is the value of cosine trigonometric function for an angle equal to 3π/2 radians. The value of cos 3pi/2 is 0.

How to Find Cos 3pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 3pi/2 can be given in terms of other trigonometric functions as:

± √(1-sin²(3pi/2))
± 1/√(1 + tan²(3pi/2))
± cot(3pi/2)/√(1 + cot²(3pi/2))
±√(cosec²(3pi/2) - 1)/cosec(3pi/2)
1/sec(3pi/2)

☛ Also check: trigonometric table

How to Find the Value of Cos 3pi/2?

The value of cos 3pi/2 can be calculated by constructing an angle of 3π/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 3pi/2 is equal to the x-coordinate (0). ∴ cos 3pi/2 = 0.

What is the Value of Cos 3pi/2 in Terms of Cosec 3pi/2?

Since the cosine function can be represented using the cosecant function, we can write cos 3pi/2 as -[√(cosec²(3pi/2) - 1)/cosec 3pi/2]. The value of cosec 3pi/2 is equal to -1.

What is the Value of Cos 3pi/2 in Terms of Sin 3pi/2?

Using trigonometric identities, we can write cos 3pi/2 in terms of sin 3pi/2 as, cos(3pi/2) = √(1 - sin²(3pi/2)). Here, the value of sin 3pi/2 is equal to -1.

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