Sin 0 Degrees

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

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

What is the Value of Sin 0 Degrees?

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

Explanation:

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

Methods to Find Value of Sin 0 Degrees

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

• Using Trigonometric Functions
• Using Unit Circle

Sin 0° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 0 degrees as:

• ± √(1-cos²(0°))
• ± tan 0°/√(1 + tan²(0°))
• ± 1/√(1 + cot²(0°))
• ± √(sec²(0°) - 1)/sec 0°
• 1/cosec 0°

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

We can use trigonometric identities to represent sin 0° as,

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

Sin 0 Degrees Using Unit Circle

To find the value of sin 0 degrees using the unit circle:

• Draw the radius of the unit circle, r to form a 0° angle with the positive x-axis. We also know that for the sin 0°, the angle 0° corresponds to the point (1, 0) on the unit circle (as it is a point on the unit circle present on the x-axis).
• The sin of 0 degrees equals the y-coordinate(0) of the point of intersection(1, 0) of the unit circle and r.

Hence the value of sin 0° = y = 0

☛ Also Check:

• sin 40 degrees
• sin 53 degrees
• sin 556 degrees
• sin 750 degrees
• sin 9 degrees
• sin 43 degrees

FAQs on Sin 0 Degrees

What is Sin 0 Degrees?

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

How to Find the Value of Sin 0 Degrees?

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

What is the Value of Sin 0° in Terms of Sec 0°?

Since the sine function can be represented using the secant function, we can write sin 0° as √(sec²(0°) - 1)/sec 0°. The value of sec 0° is equal to 1.

How to Find Sin 0° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 0° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(0°))
• ± tan 0°/√(1 + tan²(0°))
• ± 1/√(1 + cot²(0°))
• ± √(sec²(0°) - 1)/sec 0°
• 1/cosec 0°

☛ Also check: trigonometry table

What is the Value of Sin 0 Degrees in Terms of Cos 0°?

Using trigonometric identities, we can write sin 0° in terms of cos 0° as, sin(0°) = √(1-cos²(0°)). Here, the value of cos 0° is equal to 1.