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Tan pi/2

The value of tan pi/2 is not defined. Tan pi/2 radians in degrees is written as tan ((π/2) × 180°/π), i.e., tan (90°). In this article, we will discuss the methods to find the value of tan pi/2 with examples.

Tan pi/2: not defined
Tan (-pi/2): not defined
Tan pi/2 in degrees: tan (90°)

What is the Value of Tan pi/2?

The value of tan pi/2 is not defined. Tan 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
∴ tan pi/2 = tan π/2 = tan(90°) = not defined

Explanation:

For tan pi/2, the angle pi/2 lies on the positive y-axis. Thus, tan pi/2 value = not defined
Since the tangent function is a periodic function, we can represent tan pi/2 as, tan pi/2 = tan(pi/2 + n × pi), n ∈ Z.
⇒ tan pi/2 = tan 3pi/2 = tan 5pi/2 , and so on.
Note: Since, tangent is an odd function, the value of tan(-pi/2) = -tan(pi/2) = undefined.

Methods to Find Value of Tan pi/2

The value of tan pi/2 is given as not defined. We can find the value of tan pi/2 by:

Using Trigonometric Functions
Using Unit Circle

Tan pi/2 in Terms of Trigonometric Functions

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

sin(pi/2)/cos(pi/2)
± sin(pi/2)/√(1 - sin²(pi/2))
± √(1 - cos²(pi/2))/cos(pi/2)
± 1/√(cosec²(pi/2) - 1)
± √(sec²(pi/2) - 1)
1/cot(pi/2)

Note: Since pi/2 lies on the positive y-axis, the final value of tan pi/2 is not defined.

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

cot(pi/2 - pi/2) = cot 0
-cot(pi/2 + pi/2) = -cot pi
-tan (pi - pi/2) = -tan pi/2

Tan pi/2 Using Unit Circle

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

Rotate ‘r’ anticlockwise to form pi/2 angle with the positive x-axis.
The tan of pi/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 pi/2 = y/x = not defined

☛ Also Check:

Examples Using Tan pi/2

Example 1: Using the value of tan pi/2, solve: (sec²(pi/2) - 1).

Solution:
We know, (sec²(pi/2) - 1) = (tan²(pi/2)) = not defined
⇒ (sec²(pi/2) - 1) = not defined
Example 2: Find the value of tan pi/2 if cot pi/2 is 0.

Solution:
Since, tan pi/2 = 1/cot(pi/2)
⇒ tan pi/2 = 1/0 = not defined
Example 3: Find the value of 8 tan(pi/2)/10 tan(pi/4).

Solution:

Using trigonometric values, we know, tan(pi/2) = undefined and tan pi/4 = 1.
⇒ Value of 8 tan(pi/2)/10 tan(pi/4) = undefined

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FAQs on Tan pi/2

What is Tan pi/2?

Tan pi/2 is the value of tangent trigonometric function for an angle equal to π/2 radians. The value of tan pi/2 is not defined.

What is the Exact Value of tan pi/2?

The exact value of tan pi/2 is not defined.

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

Since the tangent function is the reciprocal of the cotangent function, we can write tan pi/2 as 1/cot(pi/2). The value of cot pi/2 is equal to 0.

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

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

sin(pi/2)/cos(pi/2)
± sin(pi/2)/√(1 - sin²(pi/2))
± √(1 - cos²(pi/2))/cos(pi/2)
± 1/√(cosec²(pi/2) - 1)
± √(sec²(pi/2) - 1)
1/cot(pi/2)

☛ Also check: trigonometric table

How to Find the Value of Tan pi/2?

The value of tan 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 tan pi/2 is equal to the y-coordinate(1) divided by the x-coordinate (0). ∴ tan pi/2 = not defined

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