Sin 900 Degrees

The value of sin 900 degrees is 0. Sin 900 degrees in radians is written as sin (900° × π/180°), i.e., sin (5π) or sin (15.707963. . .). In this article, we will discuss the methods to find the value of sin 900 degrees with examples.

• Sin 900°: 0
• Sin (-900 degrees): 0
• Sin 900° in radians: sin (5π) or sin (15.7079632 . . .)

What is the Value of Sin 900 Degrees?

The value of sin 900 degrees is 0. Sin 900 degrees can also be expressed using the equivalent of the given angle (900 degrees) in radians (15.70796 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 900 degrees = 900° × (π/180°) rad = 5π or 15.7079 . . .
∴ sin 900° = sin(15.7079) = 0

Explanation:

For sin 900°, the angle 900° > 360°. Given the periodic property of the sine function, we can represent it as sin(900° mod 360°) = sin(180°). The angle 900°, coterminal to angle 180°, lies on the negative x-axis.
Thus, sin 900 degrees value = 0
Similarly, sin 900° can also be written as, sin 900 degrees = (900° + n × 360°), n ∈ Z.
⇒ sin 900° = sin 1260° = sin 1620°, and so on.
Note: Since, sine is an odd function, the value of sin(-900°) = -sin(900°) = 0.

Methods to Find Value of Sin 900 Degrees

The value of sin 900° is given as 0. We can find the value of sin 900 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 900 Degrees Using Unit Circle

To find the value of sin 900 degrees using the unit circle, represent 900° in the form (2 × 360°) + 180° [∵ 900°>360°] ∵ sine is a periodic function, sin 900° = sin 180°.

• Rotate ‘r’ anticlockwise to form a 180° or 900° angle with the positive x-axis.
• The sin of 900 degrees equals the y-coordinate(0) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of sin 900° = y = 0

Sin 900° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 900 degrees as:

• ± √(1-cos²(900°))
• ± tan 900°/√(1 + tan²(900°))
• ± 1/√(1 + cot²(900°))
• ± √(sec²(900°) - 1)/sec 900°
• 1/cosec 900°

Note: Since 900° lies on the negative x-axis, the final value of sin 900° will be 0.

We can use trigonometric identities to represent sin 900° as,

• sin(180° - 900°) = sin(-720°)
• -sin(180° + 900°) = -sin 1080°
• cos(90° - 900°) = cos(-810°)
• -cos(90° + 900°) = -cos 990°

☛ Also Check:

• sin 2 degrees
• sin 60 degrees
• sin 45 degrees
• sin 900 degrees
• sin 450 degrees
• sin 29 degrees

FAQs on Sin 900 Degrees

What is Sin 900 Degrees?

Sin 900 degrees is the value of sine trigonometric function for an angle equal to 900 degrees. The value of sin 900° is 0.

How to Find the Value of Sin 900 Degrees?

The value of sin 900 degrees can be calculated by constructing an angle of 900° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of sin 900° is equal to the y-coordinate (0). ∴ sin 900° = 0.

How to Find Sin 900° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 900° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(900°))
• ± tan 900°/√(1 + tan²(900°))
• ± 1/√(1 + cot²(900°))
• ± √(sec²(900°) - 1)/sec 900°
• 1/cosec 900°

☛ Also check: trigonometry table

What is the Value of Sin 900 Degrees in Terms of Tan 900°?

We know, using trig identities, we can write sin 900° as -tan 900°/√(1 + tan²(900°)). Here, the value of tan 900° is equal to 0.

What is the Exact Value of sin 900 Degrees?

The exact value of sin 900 degrees is 0.