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Sin 360 Degrees

The value of sin 360 degrees is 0. Sin 360 degrees in radians is written as sin (360° × π/180°), i.e., sin (2π) or sin (6.283185. . .). In this article, we will discuss the methods to find the value of sin 360 degrees with examples.

Sin 360°: 0
Sin (-360 degrees): 0
Sin 360° in radians: sin (2π) or sin (6.2831853 . . .)

What is the Value of Sin 360 Degrees?

The value of sin 360 degrees is 0. Sin 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 . . .
∴ sin 360° = sin(6.2831) = 0

Explanation:

For sin 360 degrees, the angle 360° lies on the positive x-axis. Thus, sin 360° value = 0
Since the sine function is a periodic function, we can represent sin 360° as, sin 360 degrees = sin(360° + n × 360°), n ∈ Z.
⇒ sin 360° = sin 720° = sin 1080°, and so on.
Note: Since, sine is an odd function, the value of sin(-360°) = -sin(360°) = 0.

Methods to Find Value of Sin 360 Degrees

The value of sin 360° is given as 0. We can find the value of sin 360 degrees by:

Using Trigonometric Functions
Using Unit Circle

Sin 360° in Terms of Trigonometric Functions

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

± √(1-cos²(360°))
± tan 360°/√(1 + tan²(360°))
± 1/√(1 + cot²(360°))
± √(sec²(360°) - 1)/sec 360°
1/cosec 360°

Note: Since 360° lies on the positive x-axis, the final value of sin 360° will be 0.

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

sin(180° - 360°) = sin(-180°)
-sin(180° + 360°) = -sin 540°
cos(90° - 360°) = cos(-270°)
-cos(90° + 360°) = -cos 450°

Sin 360 Degrees Using Unit Circle

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

Rotate ‘r’ anticlockwise to form a 360° or 0° angle with the positive x-axis.
The sin of 360 degrees equals the y-coordinate(0) of the point of intersection (1, 0) of unit circle and r.

Hence the value of sin 360° = y = 0

☛ Also Check:

Examples Using Sin 360 Degrees

Example 1: Find the value of 5 sin(360°)/7 cos(0°).

Solution:

Using trigonometric identities, we know, sin(360°) = 0 and cos(0°) = 1.
⇒ Value of 5 sin(360°)/7 cos(0°) = 0
Example 2: Simplify: 2 (sin 360°/sin 90°)

Solution:

We know sin 360° = 0 and sin 90° = 1
⇒ 2 sin 360°/sin 90° = 2(0)
= 0
Example 3: Using the value of sin 360°, solve: (1-cos²(360°)).

Solution:
We know, (1-cos²(360°)) = (sin²(360°)) = 0
⇒ (1-cos²(360°)) = 0

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FAQs on Sin 360 Degrees

What is Sin 360 Degrees?

Sin 360 degrees is the value of sine trigonometric function for an angle equal to 360 degrees. The value of sin 360° is 0.

What is the Exact Value of sin 360 Degrees?

The exact value of sin 360 degrees is 0.

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

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

± √(1-cos²(360°))
± tan 360°/√(1 + tan²(360°))
± 1/√(1 + cot²(360°))
± √(sec²(360°) - 1)/sec 360°
1/cosec 360°

☛ Also check: trigonometry table

What is the Value of Sin 360 Degrees in Terms of Cot 360°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 360° can be written as 1/√(1 + cot²(360°)).

How to Find the Value of Sin 360 Degrees?

The value of sin 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 sin 360° is equal to the y-coordinate (0). ∴ sin 360° = 0.

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