Sec 360 Degrees

The value of Sec 360 degrees is 1. Sec 360 degrees in radians is written as sec (360° × π/180°), i.e., sec (2π) or sec (6.283185. . .). In this article, we will discuss the methods to find the value of sec 360 degrees with examples.

• Sec 360°: 1
• Sec (-360 degrees): 1
• Sec 360° in radians: sec (2π) or sec (6.2831853 . . .)

What is the Value of Sec 360 Degrees?

The value of sec 360 degrees is 1. Sec 360 degrees can also be expressed using the equivalent of the given angle (360 degrees) in radians (6.28318 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 360 degrees = 360° × (π/180°) rad = 2π or 6.2831 . . .
∴ sec 360° = sec(6.2831) = 1

Explanation:

For sec 360 degrees, the angle 360° lies on the positive x-axis. Thus sec 360° value = 1
Since the secant function is a periodic function, we can represent sec 360° as, sec 360 degrees = sec(360° + n × 360°), n ∈ Z.
⇒ sec 360° = sec 720° = sec 1080°, and so on.
Note: Since, secant is an even function, the value of sec(-360°) = sec(360°) = 1.

Methods to Find Value of Sec 360 Degrees

The value of sec 360° is given as 1. We can find the value of sec 360 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 360° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 360 degrees as:

• ± 1/√(1 - sin²(360°))
• ± √(1 + tan²(360°))
• ± √(1 + cot²(360°))/cot 360°
• ± cosec 360°/√(cosec²(360°) - 1)
• 1/cos 360°

We can use trigonometric identities to represent sec 360° as,

• -sec(180° - 360°) = -sec(-180°)
• -sec(180° + 360°) = -sec 540°
• cosec(90° + 360°) = cosec 450°
• cosec(90° - 360°) = cosec(-270°)

Note: Since 360° lies on the positive x-axis, the final value of sec 360° will be positive.

Sec 360 Degrees Using Unit Circle

To find the value of sec 360 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 0° or 360° angle with the positive x-axis.
• The sec of 360 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 360° = 1/x = 1

☛ Also Check:

• sec 135 degrees
• sec 70 degrees
• sec 15 degrees
• sec 450 degrees
• sec 390 degrees
• sec 90 degrees

FAQs on Sec 360 Degrees

What is Sec 360 Degrees?

Sec 360 degrees is the value of secant trigonometric function for an angle equal to 360 degrees. The value of sec 360° is 1.

How to Find the Value of Sec 360 Degrees?

The value of sec 360 degrees can be calculated by constructing an angle of 360° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of sec 360° is equal to the reciprocal of the x-coordinate(1). ∴ sec 360° = 1.

What is the Value of Sec 360 Degrees in Terms of Tan 360°?

We know, using trig identities, we can write sec 360° as √(1 + tan²(360°)). Here, the value of tan 360° is equal to 0.

What is the Value of Sec 360° in Terms of Cos 360°?

Since the cosine function is the reciprocal of the secant function, we can write sec 360° as 1/cos(360°). The value of cos 360° is equal to 1.

How to Find Sec 360° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 360° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(360°))
• ± √(1 + tan²(360°))
• ± √(1 + cot²(360°))/cot 360°
• ± cosec 360°/√(cosec²(360°) - 1)
• 1/cos 360°

☛ Also check: trigonometry table