Sec 0 Degrees
The value of Sec 0 degrees is 1. Sec 0 degrees in radians is written as sec (0° × π/180°), i.e., sec (0π) or sec (0). In this article, we will discuss the methods to find the value of sec 0 degrees with examples.
 Sec 0°: 1
 Sec (0 degrees): 1
 Sec 0° in radians: sec (0π) or sec (0 . . .)
What is the Value of Sec 0 Degrees?
The value of sec 0 degrees is 1. Sec 0 degrees can also be expressed using the equivalent of the given angle (0 degrees) in radians (0 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 0 degrees = 0° × (π/180°) rad = 0π or 0 . . .
∴ sec 0° = sec(0) = 1
Explanation:
For sec 0 degrees, the angle 0° lies on the positive xaxis. Thus sec 0° value = 1
Since the secant function is a periodic function, we can represent sec 0° as, sec 0 degrees = sec(0° + n × 360°), n ∈ Z.
⇒ sec 0° = sec 360° = sec 720°, and so on.
Note: Since, secant is an even function, the value of sec(0°) = sec(0°) = 1.
Methods to Find Value of Sec 0 Degrees
The value of sec 0° is given as 1. We can find the value of sec 0 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 0 Degrees Using Unit Circle
To find the value of sec 0 degrees using the unit circle:
 Draw the radius of unit circle, ‘r’, to form 0° angle with the positive xaxis.
 The sec of 0 degrees equals the reciprocal of the xcoordinate(1) of the point of intersection (1, 0) of unit circle and r.
Hence the value of sec 0° = 1/x = 1
Sec 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 0 degrees as:
 ± 1/√(1  sin²(0°))
 ± √(1 + tan²(0°))
 ± √(1 + cot²(0°))/cot 0°
 ± cosec 0°/√(cosec²(0°)  1)
 1/cos 0°
Note: Since 0° lies on the positive xaxis, the final value of sec 0° is 1.
We can use trigonometric identities to represent sec 0° as,
 sec(180°  0°) = sec 180°
 sec(180° + 0°) = sec 180°
 cosec(90° + 0°) = cosec 90°
 cosec(90°  0°) = cosec 90°
☛ Also Check:
Examples Using Sec 0 Degrees

Example 1: Simplify: 8 (sec 0°/cosec 90°)
Solution:
We know sec 0° = cosec 90°
⇒ 8 sec 0°/cosec 90° = 8 (sec 0°/sec 0°)
= 8(1) = 8 
Example 2: Using the value of sec 0°, solve: (1 + tan²(0°)).
Solution:
We know, (1 + tan²(0°)) = (sec²(0°)) = 1
⇒ (1 + tan²(0°)) = 1 
Example 3: Find the value of 1/(cos² 0°  sin² 0°). [Hint: Use sec 0° = 1]
Solution:
Using the cos 2a formula,
1/(cos² 0°  sin² 0°) = 1/cos(2 × 0°) = sec 0°
∵ sec 0° = 1
⇒ 1/(cos² 0°  sin² 0°) = 1
FAQs on Sec 0 Degrees
What is Sec 0 Degrees?
Sec 0 degrees is the value of secant trigonometric function for an angle equal to 0 degrees. The value of sec 0° is 1.
What is the Value of Sec 0 Degrees in Terms of Tan 0°?
We know, using trig identities, we can write sec 0° as √(1 + tan²(0°)). Here, the value of tan 0° is equal to 0.
How to Find Sec 0° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 0° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(0°))
 ± √(1 + tan²(0°))
 ± √(1 + cot²(0°))/cot 0°
 ± cosec 0°/√(cosec²(0°)  1)
 1/cos 0°
☛ Also check: trigonometric table
How to Find the Value of Sec 0 Degrees?
The value of sec 0 degrees can be calculated by constructing an angle of 0° with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of sec 0° is equal to the reciprocal of the xcoordinate(1). ∴ sec 0° = 1.
What is the Value of Sec 0° in Terms of Cos 0°?
Since the cosine function is the reciprocal of the secant function, we can write sec 0° as 1/cos(0°). The value of cos 0° is equal to 1.
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