Sin 720 Degrees

The value of sin 720 degrees is 0. Sin 720 degrees in radians is written as sin (720° × π/180°), i.e., sin (4π) or sin (12.566370. . .). In this article, we will discuss the methods to find the value of sin 720 degrees with examples.

• Sin 720°: 0
• Sin (-720 degrees): 0
• Sin 720° in radians: sin (4π) or sin (12.5663706 . . .)

What is the Value of Sin 720 Degrees?

The value of sin 720 degrees is 0. Sin 720 degrees can also be expressed using the equivalent of the given angle (720 degrees) in radians (12.56637 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 720 degrees = 720° × (π/180°) rad = 4π or 12.5663 . . .
∴ sin 720° = sin(12.5663) = 0

Explanation:

For sin 720°, the angle 720° > 360°. Given the periodic property of the sine function, we can represent it as sin(720° mod 360°) = sin(0°). The angle 720°, coterminal to angle 0°, lies on the positive x-axis.
Thus, sin 720 degrees value = 0
Similarly, sin 720° can also be written as, sin 720 degrees = (720° + n × 360°), n ∈ Z.
⇒ sin 720° = sin 1080° = sin 1440°, and so on.
Note: Since, sine is an odd function, the value of sin(-720°) = -sin(720°) = 0.

Methods to Find Value of Sin 720 Degrees

The value of sin 720° is given as 0. We can find the value of sin 720 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 720° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 720 degrees as:

• ± √(1-cos²(720°))
• ± tan 720°/√(1 + tan²(720°))
• ± 1/√(1 + cot²(720°))
• ± √(sec²(720°) - 1)/sec 720°
• 1/cosec 720°

Note: Since 720° lies on the positive x-axis, the final value of sin 720° will be 0.

We can use trigonometric identities to represent sin 720° as,

• sin(180° - 720°) = sin(-540°)
• -sin(180° + 720°) = -sin 900°
• cos(90° - 720°) = cos(-630°)
• -cos(90° + 720°) = -cos 810°

Sin 720 Degrees Using Unit Circle

To find the value of sin 720 degrees using the unit circle, represent 720° in the form (2 × 360°) + 0° [∵ 720°>360°] ∵ sine is a periodic function, sin 720° = sin 0°.

• Rotate ‘r’ anticlockwise to form 720° or 0° angle with the positive x-axis.
• The sin of 720 degrees equals the y-coordinate(0) of the point of intersection (1, 0) of unit circle and r.

Hence the value of sin 720° = y = 0

☛ Also Check:

• sin 90 degrees
• sin 2 degrees
• sin 1 degrees
• sin 17 degrees
• sin 130 degrees
• sin 7 degrees

FAQs on Sin 720 Degrees

What is Sin 720 Degrees?

Sin 720 degrees is the value of sine trigonometric function for an angle equal to 720 degrees. The value of sin 720° is 0.

What is the Exact Value of sin 720 Degrees?

The exact value of sin 720 degrees is 0.

What is the Value of Sin 720 Degrees in Terms of Tan 720°?

We know, using trig identities, we can write sin 720° as tan 720°/√(1 + tan²(720°)). Here, the value of tan 720° is equal to 0.

How to Find the Value of Sin 720 Degrees?

The value of sin 720 degrees can be calculated by constructing an angle of 720° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of sin 720° is equal to the y-coordinate (0). ∴ sin 720° = 0.

How to Find Sin 720° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 720° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(720°))
• ± tan 720°/√(1 + tan²(720°))
• ± 1/√(1 + cot²(720°))
• ± √(sec²(720°) - 1)/sec 720°
• 1/cosec 720°

☛ Also check: trigonometric table