Sin 540 Degrees

The value of sin 540 degrees is 0. Sin 540 degrees in radians is written as sin (540° × π/180°), i.e., sin (3π) or sin (9.424777. . .). In this article, we will discuss the methods to find the value of sin 540 degrees with examples.

• Sin 540°: 0
• Sin (-540 degrees): 0
• Sin 540° in radians: sin (3π) or sin (9.4247779 . . .)

What is the Value of Sin 540 Degrees?

The value of sin 540 degrees is 0. Sin 540 degrees can also be expressed using the equivalent of the given angle (540 degrees) in radians (9.42477 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 540 degrees = 540° × (π/180°) rad = 3π or 9.4247 . . .
∴ sin 540° = sin(9.4247) = 0

Explanation:

For sin 540°, the angle 540° > 360°. Given the periodic property of the sine function, we can represent it as sin(540° mod 360°) = sin(180°). The angle 540°, coterminal to angle 180°, lies on the negative x-axis.
Thus, sin 540 degrees value = 0
Similarly, sin 540° can also be written as, sin 540 degrees = (540° + n × 360°), n ∈ Z.
⇒ sin 540° = sin 900° = sin 1260°, and so on.
Note: Since, sine is an odd function, the value of sin(-540°) = -sin(540°) = 0.

Methods to Find Value of Sin 540 Degrees

The value of sin 540° is given as 0. We can find the value of sin 540 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 540 Degrees Using Unit Circle

To find the value of sin 540 degrees using the unit circle, represent 540° in the form (1 × 360°) + 180° [∵ 540°>360°] ∵ sine is a periodic function, sin 540° = sin 180°.

• Rotate ‘r’ anticlockwise to form a 180° or 540° angle with the positive x-axis.
• The sin of 540 degrees equals the y-coordinate(0) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of sin 540° = y = 0

Sin 540° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 540 degrees as:

• ± √(1-cos²(540°))
• ± tan 540°/√(1 + tan²(540°))
• ± 1/√(1 + cot²(540°))
• ± √(sec²(540°) - 1)/sec 540°
• 1/cosec 540°

Note: Since 540° lies on the negative x-axis, the final value of sin 540° will be 0.

We can use trigonometric identities to represent sin 540° as,

• sin(180° - 540°) = sin(-360°)
• -sin(180° + 540°) = -sin 720°
• cos(90° - 540°) = cos(-450°)
• -cos(90° + 540°) = -cos 630°

☛ Also Check:

• sin 270 degrees
• sin 35 degrees
• sin 3 degrees
• sin 255 degrees
• sin 110 degrees
• sin 26 degrees

FAQs on Sin 540 Degrees

What is Sin 540 Degrees?

Sin 540 degrees is the value of sine trigonometric function for an angle equal to 540 degrees. The value of sin 540° is 0.

What is the Exact Value of sin 540 Degrees?

The exact value of sin 540 degrees is 0.

How to Find the Value of Sin 540 Degrees?

The value of sin 540 degrees can be calculated by constructing an angle of 540° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sin 540° is equal to the y-coordinate (0). ∴ sin 540° = 0.

What is the Value of Sin 540 Degrees in Terms of Cot 540°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 540° can be written as 1/√(1 + cot²(540°)).

How to Find Sin 540° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 540° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(540°))
• ± tan 540°/√(1 + tan²(540°))
• ± 1/√(1 + cot²(540°))
• ± √(sec²(540°) - 1)/sec 540°
• 1/cosec 540°

☛ Also check: trigonometry table