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Cos 110 Degrees

The value of cos 110 degrees is -0.3420201. . .. Cos 110 degrees in radians is written as cos (110° × π/180°), i.e., cos (11π/18) or cos (1.919862. . .). In this article, we will discuss the methods to find the value of cos 110 degrees with examples.

Cos 110°: -0.3420201. . .
Cos (-110 degrees): -0.3420201. . .
Cos 110° in radians: cos (11π/18) or cos (1.9198621 . . .)

What is the Value of Cos 110 Degrees?

The value of cos 110 degrees in decimal is -0.342020143. . .. Cos 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 . . .
∴ cos 110° = cos(1.9198) = -0.3420201. . .

Explanation:

For cos 110 degrees, the angle 110° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 110° value = -0.3420201. . .
Since the cosine function is a periodic function, we can represent cos 110° as, cos 110 degrees = cos(110° + n × 360°), n ∈ Z.
⇒ cos 110° = cos 470° = cos 830°, and so on.
Note: Since, cosine is an even function, the value of cos(-110°) = cos(110°).

Methods to Find Value of Cos 110 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 110° is given as -0.34202. . .. We can find the value of cos 110 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cos 110 Degrees Using Unit Circle

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

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

Hence the value of cos 110° = x = -0.342 (approx)

Cos 110° in Terms of Trigonometric Functions

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

± √(1-sin²(110°))
± 1/√(1 + tan²(110°))
± cot 110°/√(1 + cot²(110°))
±√(cosec²(110°) - 1)/cosec 110°
1/sec 110°

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

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

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

☛ Also Check:

Examples Using Cos 110 Degrees

Example 1: Find the value of 2 cos(110°)/3 sin(-20°).

Solution:

Using trigonometric identities, we know, cos(110°) = sin(90° - 110°) = sin(-20°).
⇒ cos(110°) = sin(-20°)
⇒ Value of 2 cos(110°)/3 sin(-20°) = 2/3
Example 2: Using the value of cos 110°, solve: (1-sin²(110°)).

Solution:
We know, (1-sin²(110°)) = (cos²(110°)) = 0.117
⇒ (1-sin²(110°)) = 0.117
Example 3: Simplify: 7 (cos 110°/sin 200°)

Solution:

We know cos 110° = sin 200°
⇒ 7 cos 110°/sin 200° = 7 (cos 110°/cos 110°)
= 7(1) = 7

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FAQs on Cos 110 Degrees

What is Cos 110 Degrees?

Cos 110 degrees is the value of cosine trigonometric function for an angle equal to 110 degrees. The value of cos 110° is -0.342 (approx)

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

Using trigonometric identities, we can write cos 110° in terms of sin 110° as, cos(110°) = -√(1 - sin²(110°)). Here, the value of sin 110° is equal to 0.9397.

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

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

± √(1-sin²(110°))
± 1/√(1 + tan²(110°))
± cot 110°/√(1 + cot²(110°))
± √(cosec²(110°) - 1)/cosec 110°
1/sec 110°

☛ Also check: trigonometric table

How to Find the Value of Cos 110 Degrees?

The value of cos 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 cos 110° is equal to the x-coordinate (-0.342). ∴ cos 110° = -0.342.

What is the Exact Value of cos 110 Degrees?

The exact value of cos 110 degrees can be given accurately up to 8 decimal places as -0.34202014.

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