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 y-axis. 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 y-axis, 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 x-axis.
• The tan of 3pi/2 equals the y-coordinate(-1) divided by the x-coordinate(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:

• cot 2pi/3
• tan 11pi/12
• tan 5pi/2
• sin 2pi/5
• cos 17pi/12
• cot pi/3

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 x-axis, 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 y-coordinate(-1) divided by the x-coordinate (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.