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 xaxis. 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 xaxis, 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 xaxis.
 The sec of pi equals the reciprocal of the xcoordinate(1) of the point of intersection (1, 0) of unit circle and r.
Hence the value of sec pi = 1/x = 1
☛ Also Check:
Examples Using Sec pi

Example 1: Simplify: 3 (sec(pi)/cosec(3pi/2))
Solution:
We know sec pi = cosec 3pi/2
⇒ 3 sec(pi)/cosec(3pi/2) = 3 (sec(pi)/sec(pi))
= 3(1) = 3 
Example 2: Find the value of sec pi if cos pi is 1.
Solution:
Since, sec pi = 1/cos(pi)
⇒ sec pi = 1/(1) = 1 
Example 3: Find the value of 2 sec(pi)/3 cosec(pi/2).
Solution:
Using trigonometric identities, we know, sec(pi) = cosec(pi/2  pi) = cosec(pi/2)
⇒ sec(pi) = cosec(pi/2)
⇒ Value of 2 sec(pi)/3 cosec(pi/2) = 2/3
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 xaxis, 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 xcoordinate(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.
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