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 tát 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°).

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We know, using radian to tát 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 sánh on.
Note: Since, tangent is an odd function, the value of tan(-pi/2) = -tan(pi/2) = undefined.

Methods to tát 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 tát represent tan pi/2 as,

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• 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 tát size 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:

• cos 2pi
• cos 4pi
• cos 7pi/6
• cos 11pi/4
• tan 5pi/12
• cos 5pi/8

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 tát 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 tát 0.

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How to tát 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 tát 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 tát the y-coordinate(1) divided by the x-coordinate (0). ∴ tan pi/2 = not defined