Tan 3pi/2
The value of tan 3pi/2 is not defined. Tan 3pi/2 radians in degrees is written as tan ((3π/2) × 180°/π), i.e., tan (270°). In this article, we will discuss the methods to find the value of tan 3pi/2 with examples.
 Tan 3pi/2: not defined
 Tan (3pi/2): not defined
 Tan 3pi/2 in degrees: tan (270°)
What is the Value of Tan 3pi/2?
The value of tan 3pi/2 is not defined. Tan 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
∴ tan 3pi/2 = tan 3π/2 = tan(270°) = not defined
Explanation:
For tan 3pi/2, the angle 3pi/2 lies on the negative yaxis. Thus, tan 3pi/2 value = not defined
Since the tangent function is a periodic function, we can represent tan 3pi/2 as, tan 3pi/2 = tan(3pi/2 + n × pi), n ∈ Z.
⇒ tan 3pi/2 = tan 5pi/2 = tan 7pi/2 , and so on.
Note: Since, tangent is an odd function, the value of tan(3pi/2) = tan(3pi/2) = not defined.
Methods to Find Value of Tan 3pi/2
The value of tan 3pi/2 is given as not defined. We can find the value of tan 3pi/2 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 3pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 3pi/2 as:
 sin(3pi/2)/cos(3pi/2)
 ± sin(3pi/2)/√(1  sin²(3pi/2))
 ± √(1  cos²(3pi/2))/cos(3pi/2)
 ± 1/√(cosec²(3pi/2)  1)
 ± √(sec²(3pi/2)  1)
 1/cot(3pi/2)
Note: Since 3pi/2 lies on the negative yaxis, the final value of tan 3pi/2 is not defined.
We can use trigonometric identities to represent tan 3pi/2 as,
 cot(pi/2  3pi/2) = cot(pi)
 cot(pi/2 + 3pi/2) = cot 2pi
 tan (pi  3pi/2) = tan(pi/2)
Tan 3pi/2 Using Unit Circle
To find the value of tan 3π/2 using the unit circle:
 Rotate ‘r’ anticlockwise to form 3pi/2 angle with the positive xaxis.
 The tan of 3pi/2 equals the ycoordinate(1) divided by the xcoordinate(0) of the point of intersection (0, 1) of unit circle and r.
Hence the value of tan 3pi/2 = y/x = not defined
☛ Also Check:
Examples Using Tan 3pi/2

Example 1: Find the value of 4 tan(3pi/2)/7 tan(pi/4).
Solution:
Using trigonometric values, we know, tan(3pi/2) = undefined and tan(pi/4) = 1.
⇒ Value of 4 tan(3pi/2)/7 tan(pi/4) = undefined 
Example 2: Find the value of tan 3pi/2 if cot 3pi/2 is 0.
Solution:
Since, tan 3pi/2 = 1/cot(3pi/2)
⇒ tan 3pi/2 = 1/0 = not defined 
Example 3: Simplify: 5 (tan(3pi/2)/cot(pi/4))
Solution:
We know tan 3pi/2 = undefined and cot(pi/4) = 1
⇒ 5 tan(3pi/2)/cot(pi/4) = undefined
FAQs on Tan 3pi/2
What is Tan 3pi/2?
Tan 3pi/2 is the value of tangent trigonometric function for an angle equal to 3π/2 radians. The value of tan 3pi/2 is not defined.
What is the Value of Tan 3pi/2 in Terms of Sin 3pi/2?
Using trigonometric identities, we can write tan 3pi/2 in terms of sin 3pi/2 as, tan(3pi/2) = sin(3pi/2)/√(1  sin²(3pi/2)) . Here, the value of sin 3pi/2 is equal to 1.
How to Find the Value of Tan 3pi/2?
The value of tan 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 tan 3pi/2 is equal to the ycoordinate(1) divided by the xcoordinate (0). ∴ tan 3pi/2 = not defined
How to Find Tan 3pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 3pi/2 can be given in terms of other trigonometric functions as:
 sin(3pi/2)/cos(3pi/2)
 ± sin(3pi/2)/√(1  sin²(3pi/2))
 ± √(1  cos²(3pi/2))/cos(3pi/2)
 ± 1/√(cosec²(3pi/2)  1)
 ± √(sec²(3pi/2)  1)
 1/cot(3pi/2)
☛ Also check: trigonometry table
What is the Value of Tan 3pi/2 in Terms of Cosec 3pi/2?
Since the tangent function can be represented using the cosecant function, we can write tan 3pi/2 as 1/√(cosec²(3pi/2)  1). The value of cosec 3pi/2 is equal to 1.
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