Sin 99 Degrees

The value of sin 99 degrees is 0.9876883. . .. Sin 99 degrees in radians is written as sin (99° × π/180°), i.e., sin (11π/20) or sin (1.727875. . .). In this article, we will discuss the methods to find the value of sin 99 degrees with examples.

• Sin 99°: 0.9876883. . .
• Sin (-99 degrees): -0.9876883. . .
• Sin 99° in radians: sin (11π/20) or sin (1.7278759 . . .)

What is the Value of Sin 99 Degrees?

The value of sin 99 degrees in decimal is 0.987688340. . .. Sin 99 degrees can also be expressed using the equivalent of the given angle (99 degrees) in radians (1.72787 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 99 degrees = 99° × (π/180°) rad = 11π/20 or 1.7278 . . .
∴ sin 99° = sin(1.7278) = 0.9876883. . .

Explanation:

For sin 99 degrees, the angle 99° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 99° value = 0.9876883. . .
Since the sine function is a periodic function, we can represent sin 99° as, sin 99 degrees = sin(99° + n × 360°), n ∈ Z.
⇒ sin 99° = sin 459° = sin 819°, and so on.
Note: Since, sine is an odd function, the value of sin(-99°) = -sin(99°).

Methods to Find Value of Sin 99 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 99° is given as 0.98768. . .. We can find the value of sin 99 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 99° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 99 degrees as:

• ± √(1-cos²(99°))
• ± tan 99°/√(1 + tan²(99°))
• ± 1/√(1 + cot²(99°))
• ± √(sec²(99°) - 1)/sec 99°
• 1/cosec 99°

Note: Since 99° lies in the 2nd Quadrant, the final value of sin 99° will be positive.

We can use trigonometric identities to represent sin 99° as,

• sin(180° - 99°) = sin 81°
• -sin(180° + 99°) = -sin 279°
• cos(90° - 99°) = cos(-9°)
• -cos(90° + 99°) = -cos 189°

Sin 99 Degrees Using Unit Circle

To find the value of sin 99 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 99° angle with the positive x-axis.
• The sin of 99 degrees equals the y-coordinate(0.9877) of the point of intersection (-0.1564, 0.9877) of unit circle and r.

Hence the value of sin 99° = y = 0.9877 (approx)

☛ Also Check:

• sin 1 degrees
• sin 90 degrees
• sin 15 degrees
• sin 71 degrees
• sin 240 degrees
• sin 105 degrees

FAQs on Sin 99 Degrees

What is Sin 99 Degrees?

Sin 99 degrees is the value of sine trigonometric function for an angle equal to 99 degrees. The value of sin 99° is 0.9877 (approx).

What is the Value of Sin 99 Degrees in Terms of Tan 99°?

We know, using trig identities, we can write sin 99° as -tan 99°/√(1 + tan²(99°)). Here, the value of tan 99° is equal to -6.313751.

How to Find the Value of Sin 99 Degrees?

The value of sin 99 degrees can be calculated by constructing an angle of 99° with the x-axis, and then finding the coordinates of the corresponding point (-0.1564, 0.9877) on the unit circle. The value of sin 99° is equal to the y-coordinate (0.9877). ∴ sin 99° = 0.9877.

How to Find Sin 99° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 99° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(99°))
• ± tan 99°/√(1 + tan²(99°))
• ± 1/√(1 + cot²(99°))
• ± √(sec²(99°) - 1)/sec 99°
• 1/cosec 99°

☛ Also check: trigonometry table

What is the Exact Value of sin 99 Degrees?

The exact value of sin 99 degrees can be given accurately up to 8 decimal places as 0.98768834.