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Cosec 3pi/2
The value of cosec 3pi/2 is 1. Cosec 3pi/2 radians in degrees is written as csc ((3π/2) × 180°/π), i.e., csc (270°). In this article, we will discuss the methods to find the value of csc 3pi/2 with examples.
 Cosec 3pi/2: 1
 Cosec (3pi/2): 1
 Cosec 3pi/2 in degrees: csc (270°)
What is the Value of Cosec 3pi/2?
The value of cosec 3pi/2 is 1. Cosec 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
∴ csc 3pi/2 = csc 3π/2 = cosec(270°) = 1
Explanation:
For cosec 3pi/2, the angle 3pi/2 lies on the negative yaxis. Thus, csc 3pi/2 value = 1
Since the cosecant function is a periodic function, we can represent cosec 3pi/2 as, cosec 3pi/2 = cosec(3pi/2 + n × 2pi), n ∈ Z.
⇒ csc 3pi/2 = cosec 7pi/2 = csc 11pi/2 , and so on.
Note: Since, cosecant is an odd function, the value of cosec(3pi/2) = cosec(3pi/2).
Methods to Find Value of Cosec 3pi/2
The value of csc 3pi/2 is given as 1. We can find the value of cosec 3pi/2 by:
 Using Trigonometric Functions
 Using Unit Circle
Cosec 3pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the csc 3pi/2 as:
 ± 1/√(1cos²(3pi/2))
 ± √(1 + tan²(3pi/2))/tan(3pi/2)
 ± √(1 + cot²(3pi/2))
 ± sec(3pi/2)/√(sec²(3pi/2)  1))
 1/sin(3pi/2)
Note: Since 3pi/2 lies on the negative yaxis, the final value of cosec 3pi/2 is 1.
We can use trigonometric identities to represent csc 3pi/2 as,
 csc(pi  3pi/2) = csc(pi/2)
 cosec(pi + 3pi/2) = cosec 5pi/2
 sec(pi/2  3pi/2) = sec(pi)
 sec(pi/2 + 3pi/2) = sec 2pi
Cosec 3pi/2 Using Unit Circle
To find the value of csc 3π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form 3pi/2 angle with the positive xaxis.
 The cosec of 3pi/2 equals the reciprocal of the ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of csc 3pi/2 = 1/y = 1
☛ Also Check:
Examples Using Cosec 3pi/2

Example 1: Find the value of 3 csc(3pi/2)/9 sec(pi).
Solution:
Using trigonometric identities, we know, csc(3pi/2) = sec(pi/2  3pi/2) = sec(pi).
⇒ csc(3pi/2) = sec(pi)
⇒ Value of 3 cosec(3pi/2)/9 sec(pi) = 1/3 
Example 2: Simplify: 10 (csc(3pi/2)/csc(7pi/2))
Solution:
We know csc 3pi/2 = csc 7pi/2
⇒ 10 csc(3pi/2)/csc(7pi/2) = 10(csc(3pi/2)/csc(3pi/2))
= 10(1) = 10 
Example 3: Find the value of csc 3pi/2 if sin 3pi/2 is 1.
Solution:
Since, csc 3pi/2 = 1/sin(3pi/2)
⇒ csc 3pi/2 = 1/(1) = 1
FAQs on Cosec 3pi/2
What is Cosec 3pi/2?
Cosec 3pi/2 is the value of cosecant trigonometric function for an angle equal to 3π/2. The value of cosec 3pi/2 is 1.
How to Find Cosec 3pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of csc 3pi/2 can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(3pi/2))
 ± √(1 + tan²(3pi/2))/tan(3pi/2)
 ± √(1 + cot²(3pi/2))
 ± sec(3pi/2)/√(sec²(3pi/2)  1))
 1/sin(3pi/2)
☛ Also check: trigonometric table
What is the Value of Cosec 3pi/2 in Terms of Tan 3pi/2?
We know, using trig identities, we can write csc 3pi/2 as √(1 + tan²(3pi/2))/tan 3pi/2. Here, the value of tan 3pi/2 is equal to not defined.
What is the Exact Value of Cosec 3pi/2?
The exact value of csc 3pi/2 is 1.
How to Find the Value of Cosec 3pi/2?
The value of csc 3pi/2 can be calculated by constructing an angle of 3π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of csc 3pi/2 is equal to the reciprocal of the ycoordinate (1). ∴ csc 3pi/2 = 1.
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