Sin 110 Degrees

The value of sin 110 degrees is 0.9396926. . .. Sin 110 degrees in radians is written as sin (110° × π/180°), i.e., sin (11π/18) or sin (1.919862. . .). In this article, we will discuss the methods to find the value of sin 110 degrees with examples.

• Sin 110°: 0.9396926. . .
• Sin (-110 degrees): -0.9396926. . .
• Sin 110° in radians: sin (11π/18) or sin (1.9198621 . . .)

What is the Value of Sin 110 Degrees?

The value of sin 110 degrees in decimal is 0.939692620. . .. Sin 110 degrees can also be expressed using the equivalent of the given angle (110 degrees) in radians (1.91986 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 110 degrees = 110° × (π/180°) rad = 11π/18 or 1.9198 . . .
∴ sin 110° = sin(1.9198) = 0.9396926. . .

Explanation:

For sin 110 degrees, the angle 110° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 110° value = 0.9396926. . .
Since the sine function is a periodic function, we can represent sin 110° as, sin 110 degrees = sin(110° + n × 360°), n ∈ Z.
⇒ sin 110° = sin 470° = sin 830°, and so on.
Note: Since, sine is an odd function, the value of sin(-110°) = -sin(110°).

Methods to Find Value of Sin 110 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 110° is given as 0.93969. . .. We can find the value of sin 110 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 110° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 110 degrees as:

• ± √(1-cos²(110°))
• ± tan 110°/√(1 + tan²(110°))
• ± 1/√(1 + cot²(110°))
• ± √(sec²(110°) - 1)/sec 110°
• 1/cosec 110°

Note: Since 110° lies in the 2nd Quadrant, the final value of sin 110° will be positive.

We can use trigonometric identities to represent sin 110° as,

• sin(180° - 110°) = sin 70°
• -sin(180° + 110°) = -sin 290°
• cos(90° - 110°) = cos(-20°)
• -cos(90° + 110°) = -cos 200°

Sin 110 Degrees Using Unit Circle

To find the value of sin 110 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 110° angle with the positive x-axis.
• The sin of 110 degrees equals the y-coordinate(0.9397) of the point of intersection (-0.342, 0.9397) of unit circle and r.

Hence the value of sin 110° = y = 0.9397 (approx)

☛ Also Check:

• sin 11 degrees
• sin 50 degrees
• sin 104 degrees
• sin 1125 degrees
• sin 1000 degrees
• sin 65 degrees

FAQs on Sin 110 Degrees

What is Sin 110 Degrees?

Sin 110 degrees is the value of sine trigonometric function for an angle equal to 110 degrees. The value of sin 110° is 0.9397 (approx).

How to Find the Value of Sin 110 Degrees?

The value of sin 110 degrees can be calculated by constructing an angle of 110° with the x-axis, and then finding the coordinates of the corresponding point (-0.342, 0.9397) on the unit circle. The value of sin 110° is equal to the y-coordinate (0.9397). ∴ sin 110° = 0.9397.

What is the Exact Value of sin 110 Degrees?

The exact value of sin 110 degrees can be given accurately up to 8 decimal places as 0.93969262.

What is the Value of Sin 110 Degrees in Terms of Cot 110°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 110° can be written as 1/√(1 + cot²(110°)). Here, the value of cot 110° is equal to -0.36397.

How to Find Sin 110° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 110° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(110°))
• ± tan 110°/√(1 + tan²(110°))
• ± 1/√(1 + cot²(110°))
• ± √(sec²(110°) - 1)/sec 110°
• 1/cosec 110°

☛ Also check: trigonometry table