Sin 180 Degrees

The value of sin 180 degrees is 0. Sin 180 degrees in radians is written as sin (180° × π/180°), i.e., sin (π) or sin (3.141592. . .). In this article, we will discuss the methods to find the value of sin 180 degrees with examples.

• Sin 180°: 0
• Sin (-180 degrees): 0
• Sin 180° in radians: sin (π) or sin (3.1415926 . . .)

What is the Value of Sin 180 Degrees?

The value of sin 180 degrees is 0. Sin 180 degrees can also be expressed using the equivalent of the given angle (180 degrees) in radians (3.14159 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 180 degrees = 180° × (π/180°) rad = π or 3.1415 . . .
∴ sin 180° = sin(3.1415) = 0

Explanation:

For sin 180 degrees, the angle 180° lies on the negative x-axis. Thus, sin 180° value = 0
Since the sine function is a periodic function, we can represent sin 180° as, sin 180 degrees = sin(180° + n × 360°), n ∈ Z.
⇒ sin 180° = sin 540° = sin 900°, and so on.
Note: Since, sine is an odd function, the value of sin(-180°) = -sin(180°) = 0.

Methods to Find Value of Sin 180 Degrees

The value of sin 180° is given as 0. We can find the value of sin 180 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 180 Degrees Using Unit Circle

To find the value of sin 180 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 180° angle with the positive x-axis.
• The sin of 180 degrees equals the y-coordinate(0) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of sin 180° = y = 0

Sin 180° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 180 degrees as:

• ± √(1-cos²(180°))
• ± tan 180°/√(1 + tan²(180°))
• ± 1/√(1 + cot²(180°))
• ± √(sec²(180°) - 1)/sec 180°
• 1/cosec 180°

Note: Since 180° lies on the negative x-axis, the final value of sin 180° will be 0.

We can use trigonometric identities to represent sin 180° as,

• sin(180° - 180°) = sin 0°
• -sin(180° + 180°) = -sin 360°
• cos(90° - 180°) = cos(-90°)
• -cos(90° + 180°) = -cos 270°

☛ Also Check:

• sin 45 degrees
• sin 20 degrees
• sin 135 degrees
• sin 144 degrees
• sin 44 degrees
• sin 16 degrees

FAQs on Sin 180 Degrees

What is Sin 180 Degrees?

Sin 180 degrees is the value of sine trigonometric function for an angle equal to 180 degrees. The value of sin 180° is 0.

How to Find Sin 180° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 180° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(180°))
• ± tan 180°/√(1 + tan²(180°))
• ± 1/√(1 + cot²(180°))
• ± √(sec²(180°) - 1)/sec 180°
• 1/cosec 180°

☛ Also check: trigonometric table

What is the Value of Sin 180 Degrees in Terms of Cosec 180°?

We can represent the sine function in terms of the cosecant function using trig identities, sin 180° can be written as 1/cosec(180°).

What is the Value of Sin 180° in Terms of Sec 180°?

Since the sine function can be represented using the secant function, we can write sin 180° as -√(sec²(180°) - 1)/sec 180°. The value of sec 180° is equal to -1.

How to Find the Value of Sin 180 Degrees?

The value of sin 180 degrees can be calculated by constructing an angle of 180° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sin 180° is equal to the y-coordinate (0). ∴ sin 180° = 0.