Sec pi

The value of sec pi is -1. Sec pi radians in degrees is written as sec ((π) × 180°/π), i.e., sec (180°). In this article, we will discuss the methods to find the value of sec pi with examples.

• Sec pi: -1
• Sec (-pi): -1
• Sec pi in degrees: sec (180°)

What is the Value of Sec pi?

The value of sec pi is -1. Sec pi can also be expressed using the equivalent of the given angle (pi) in degrees (180°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi radians = pi × (180°/pi) = 180° or 180 degrees
∴ sec pi = sec π = sec(180°) = -1

Explanation:

For sec pi, the angle pi lies on the negative x-axis. Thus, sec pi value = -1
Since the secant function is a periodic function, we can represent sec pi as, sec pi = sec(pi + n × 2pi), n ∈ Z.
⇒ sec pi = sec 3pi = sec 5pi , and so on.
Note: Since, secant is an even function, the value of sec(-pi) = sec(pi).

Methods to Find Value of Sec pi

The value of sec pi is given as -1. We can find the value of sec pi by:

• Using Trigonometric Functions
• Using Unit Circle

Sec pi in Terms of Trigonometric Functions

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

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

Note: Since pi lies on the negative x-axis, the final value of sec pi is -1.

We can use trigonometric identities to represent sec pi as,

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

Sec pi Using Unit Circle

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

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

Hence the value of sec pi = 1/x = -1

☛ Also Check:

• cos 7pi/12
• cot 15pi/4
• sec pi/3
• tan 7pi/8
• cos 3pi/2
• tan 5pi/6

FAQs on Sec pi

What is Sec pi?

Sec pi is the value of secant trigonometric function for an angle equal to π. The value of sec pi is -1.

What is the Exact Value of Sec pi?

The exact value of sec pi is -1.

How to Find the Value of Sec pi?

The value of sec pi can be calculated by constructing an angle of π radians with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sec pi is equal to the reciprocal of the x-coordinate(-1). ∴ sec pi = -1.

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

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

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

☛ Also check: trigonometric table

What is the Value of Sec pi in Terms of Sin pi?

Using trigonometric identities, we can write sec pi in terms of sin pi as, sec(pi) = -1/√(1 - sin²(pi)). Here, the value of sin pi is equal to 0.