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Sec pi/3
The value of sec pi/3 is 2. Sec pi/3 radians in degrees is written as sec ((π/3) × 180°/π), i.e., sec (60°). In this article, we will discuss the methods to find the value of sec pi/3 with examples.
 Sec pi/3: 2
 Sec (pi/3): 2
 Sec pi/3 in degrees: sec (60°)
What is the Value of Sec pi/3?
The value of sec pi/3 is 2. Sec pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/3 radians = pi/3 × (180°/pi) = 60° or 60 degrees
∴ sec pi/3 = sec π/3 = sec(60°) = 2
Explanation:
For sec pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since secant function is positive in the first quadrant, thus sec pi/3 value = 2
Since the secant function is a periodic function, we can represent sec pi/3 as, sec pi/3 = sec(pi/3 + n × 2pi), n ∈ Z.
⇒ sec pi/3 = sec 7pi/3 = sec 13pi/3 , and so on.
Note: Since, secant is an even function, the value of sec(pi/3) = sec(pi/3).
Methods to Find Value of Sec pi/3
The secant function is positive in the 1st quadrant. The value of sec pi/3 is given as 2. We can find the value of sec pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Sec pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec pi/3 as:
 ± 1/√(1 – sin²(pi/3))
 ± √(1 + tan²(pi/3))
 ± √(1 + cot²(pi/3))/cot(pi/3)
 ± cosec(pi/3)/√(cosec²(pi/3) – 1)
 1/cos(pi/3)
Note: Since pi/3 lies in the 1st Quadrant, the final value of sec pi/3 will be positive.
We can use trigonometric identities to represent sec pi/3 as,
 sec(pi – pi/3) = sec 2pi/3
 sec(pi + pi/3) = sec 4pi/3
 cosec(pi/2 + pi/3) = cosec 5pi/6
 cosec(pi/2 – pi/3) = cosec pi/6
Sec pi/3 Using Unit Circle
To find the value of sec π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/3 angle with the positive xaxis.
 The sec of pi/3 equals the reciprocal of the xcoordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of sec pi/3 = 1/x = 2
☛ Also Check:
Examples Using Sec pi/3

Example 1: Find the value of 2 sec(pi/3)/3 cosec(pi/6).
Solution:
Using trigonometric identities, we know, sec(pi/3) = cosec(pi/2 – pi/3) = cosec pi/6
⇒ sec(pi/3) = cosec(pi/6)
⇒ Value of 2 sec(pi/3)/3 cosec(pi/6) = 2/3 
Example 2: Find the value of 1/(cos² pi/6 – sin² pi/6). [Hint: Use sec pi/3 = 2]
Solution:
Using the cos 2a formula,
1/(cos² pi/6 – sin² pi/6) = 1/cos(2 × pi/6) = sec pi/3
∵ sec pi/3 = 2
⇒ 1/(cos² pi/6 – sin² pi/6) = 2 
Example 3: Simplify: 8 (sec(pi/3)/cosec(5pi/6))
Solution:
We know sec pi/3 = cosec 5pi/6
⇒ 8 sec(pi/3)/cosec(5pi/6) = 8 (sec(pi/3)/sec(pi/3))
= 8(1) = 8
FAQs on Sec pi/3
What is Sec pi/3?
Sec pi/3 is the value of secant trigonometric function for an angle equal to π/3. The value of sec pi/3 is 2.
What is the Value of Sec pi/3 in Terms of Tan pi/3?
We know, using trig identities, we can write sec pi/3 as √(1 + tan²(pi/3)). Here, the value of tan pi/3 is equal to 1.7321.
How to Find Sec pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec pi/3 can be given in terms of other trigonometric functions as:
 ± 1/√(1 – sin²(pi/3))
 ± √(1 + tan²(pi/3))
 ± √(1 + cot²(pi/3))/cot(pi/3)
 ± cosec(pi/3)/√(cosec²(pi/3) – 1)
 1/cos(pi/3)
☛ Also check: trigonometry table
What is the Value of Sec pi/3 in Terms of Cos pi/3?
Since the cosine function is the reciprocal of the secant function, we can write sec pi/3 as 1/cos(pi/3). The value of cos pi/3 is equal to 0.5.
How to Find the Value of Sec pi/3?
The value of sec pi/3 can be calculated by constructing an angle of π/3 radians with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of sec pi/3 is equal to the reciprocal of the xcoordinate(0.5). ∴ sec pi/3 = 2.
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