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Sec pi/2

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

Sec pi/2: not defined
Sec (-pi/2): not defined
Sec pi/2 in degrees: sec (90°)

What is the Value of Sec pi/2?

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

Explanation:

For sec pi/2, the angle pi/2 lies on the positive y-axis. Thus, sec pi/2 value = not defined
Since the secant function is a periodic function, we can represent sec pi/2 as, sec pi/2 = sec(pi/2 + n × 2pi), n ∈ Z.
⇒ sec pi/2 = sec 5pi/2 = sec 9pi/2 , and so on.
Note: Since, secant is an even function, the value of sec(-pi/2) = sec(pi/2) = not defined.

Methods to Find Value of Sec pi/2

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

Using Unit Circle
Using Trigonometric Functions

Sec pi/2 Using Unit Circle

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

Rotate ‘r’ anticlockwise to form pi/2 angle with the positive x-axis.
The sec of pi/2 equals the reciprocal of the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sec pi/2 = 1/x = not defined

Sec pi/2 in Terms of Trigonometric Functions

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

± 1/√(1 - sin²(pi/2))
± √(1 + tan²(pi/2))
± √(1 + cot²(pi/2))/cot(pi/2)
± cosec(pi/2)/√(cosec²(pi/2) - 1)
1/cos(pi/2)

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

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

-sec(pi - pi/2) = -sec pi/2
-sec(pi + pi/2) = -sec 3pi/2
cosec(pi/2 + pi/2) = cosec pi
cosec(pi/2 - pi/2) = cosec 0

☛ Also Check:

Examples Using Sec pi/2

Example 1: Find the value of 1/(cos² pi/4 - sin² pi/4). [Hint: Use sec pi/2 = not defined]

Solution:

Using the cos 2a formula,
1/(cos² pi/4 - sin² pi/4) = 1/cos(2 × pi/4) = sec pi/2
∵ sec pi/2 = not defined
⇒ 1/(cos² pi/4 - sin² pi/4) = not defined
Example 2: Find the value of sec pi/2 if cos pi/2 is 0.

Solution:
Since, sec pi/2 = 1/cos(pi/2)
⇒ sec pi/2 = 1/0 = not defined
Example 3: Simplify: 6 (sec(pi/2)/cosec(pi/2))

Solution:

We know sec pi/2 = not defined; cosec pi/2 = 1
⇒ 6 sec(pi/2)/cosec(pi/2) = not defined

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FAQs on Sec pi/2

What is Sec pi/2?

Sec pi/2 is the value of secant trigonometric function for an angle equal to π/2. The value of sec pi/2 is not defined.

How to Find the Value of Sec pi/2?

The value of sec 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 sec pi/2 is equal to the reciprocal of the x-coordinate(0). ∴ sec pi/2 = not defined.

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

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

± 1/√(1 - sin²(pi/2))
± √(1 + tan²(pi/2))
± √(1 + cot²(pi/2))/cot(pi/2)
± cosec(pi/2)/√(cosec²(pi/2) - 1)
1/cos(pi/2)

☛ Also check: trigonometric table

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

We can represent the secant function in terms of the cotangent function using trig identities, sec pi/2 can be written as √(1 + cot²(pi/2))/cot pi/2. Here, the value of cot pi/2 is equal to 0.

What is the Exact Value of Sec pi/2?

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

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