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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 x-axis. 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 x-axis.
The sec of 0 degrees 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 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 x-axis, 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

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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/√(1-sin²(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 x-axis, 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 x-coordinate(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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