Sin 100 Degrees

The value of sin 100 degrees is 0.9848077. . .. Sin 100 degrees in radians is written as sin (100° × π/180°), i.e., sin (5π/9) or sin (1.745329. . .). In this article, we will discuss the methods to find the value of sin 100 degrees with examples.

• Sin 100°: 0.9848077. . .
• Sin (-100 degrees): -0.9848077. . .
• Sin 100° in radians: sin (5π/9) or sin (1.7453292 . . .)

What is the Value of Sin 100 Degrees?

The value of sin 100 degrees in decimal is 0.984807753. . .. Sin 100 degrees can also be expressed using the equivalent of the given angle (100 degrees) in radians (1.74532 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 100 degrees = 100° × (π/180°) rad = 5π/9 or 1.7453 . . .
∴ sin 100° = sin(1.7453) = 0.9848077. . .

Explanation:

For sin 100 degrees, the angle 100° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 100° value = 0.9848077. . .
Since the sine function is a periodic function, we can represent sin 100° as, sin 100 degrees = sin(100° + n × 360°), n ∈ Z.
⇒ sin 100° = sin 460° = sin 820°, and so on.
Note: Since, sine is an odd function, the value of sin(-100°) = -sin(100°).

Methods to Find Value of Sin 100 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 100° is given as 0.98480. . .. We can find the value of sin 100 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 100° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 100 degrees as:

• ± √(1-cos²(100°))
• ± tan 100°/√(1 + tan²(100°))
• ± 1/√(1 + cot²(100°))
• ± √(sec²(100°) - 1)/sec 100°
• 1/cosec 100°

Note: Since 100° lies in the 2nd Quadrant, the final value of sin 100° will be positive.

We can use trigonometric identities to represent sin 100° as,

• sin(180° - 100°) = sin 80°
• -sin(180° + 100°) = -sin 280°
• cos(90° - 100°) = cos(-10°)
• -cos(90° + 100°) = -cos 190°

Sin 100 Degrees Using Unit Circle

To find the value of sin 100 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 100° angle with the positive x-axis.
• The sin of 100 degrees equals the y-coordinate(0.9848) of the point of intersection (-0.1736, 0.9848) of unit circle and r.

Hence the value of sin 100° = y = 0.9848 (approx)

☛ Also Check:

• sin 120 degrees
• sin 360 degrees
• sin 45 degrees
• sin 57 degrees
• sin 720 degrees
• sin 41 degrees

FAQs on Sin 100 Degrees

What is Sin 100 Degrees?

Sin 100 degrees is the value of sine trigonometric function for an angle equal to 100 degrees. The value of sin 100° is 0.9848 (approx).

What is the Value of Sin 100 Degrees in Terms of Tan 100°?

We know, using trig identities, we can write sin 100° as -tan 100°/√(1 + tan²(100°)). Here, the value of tan 100° is equal to -5.671281.

How to Find Sin 100° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 100° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(100°))
• ± tan 100°/√(1 + tan²(100°))
• ± 1/√(1 + cot²(100°))
• ± √(sec²(100°) - 1)/sec 100°
• 1/cosec 100°

☛ Also check: trigonometry table

What is the Exact Value of sin 100 Degrees?

The exact value of sin 100 degrees can be given accurately up to 8 decimal places as 0.98480775.

How to Find the Value of Sin 100 Degrees?

The value of sin 100 degrees can be calculated by constructing an angle of 100° with the x-axis, and then finding the coordinates of the corresponding point (-0.1736, 0.9848) on the unit circle. The value of sin 100° is equal to the y-coordinate (0.9848). ∴ sin 100° = 0.9848.