Cos 100 Degrees

The value of cos 100 degrees is -0.1736481. . .. Cos 100 degrees in radians is written as cos (100° × π/180°), i.e., cos (5π/9) or cos (1.745329. . .). In this article, we will discuss the methods to find the value of cos 100 degrees with examples.

• Cos 100°: -0.1736481. . .
• Cos (-100 degrees): -0.1736481. . .
• Cos 100° in radians: cos (5π/9) or cos (1.7453292 . . .)

What is the Value of Cos 100 Degrees?

The value of cos 100 degrees in decimal is -0.173648177. . .. Cos 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 . . .
∴ cos 100° = cos(1.7453) = -0.1736481. . .

Explanation:

For cos 100 degrees, the angle 100° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 100° value = -0.1736481. . .
Since the cosine function is a periodic function, we can represent cos 100° as, cos 100 degrees = cos(100° + n × 360°), n ∈ Z.
⇒ cos 100° = cos 460° = cos 820°, and so on.
Note: Since, cosine is an even function, the value of cos(-100°) = cos(100°).

Methods to Find Value of Cos 100 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 100° is given as -0.17364. . .. We can find the value of cos 100 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 100° in Terms of Trigonometric Functions

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

• ± √(1-sin²(100°))
• ± 1/√(1 + tan²(100°))
• ± cot 100°/√(1 + cot²(100°))
• ±√(cosec²(100°) - 1)/cosec 100°
• 1/sec 100°

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

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

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

Cos 100 Degrees Using Unit Circle

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

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

Hence the value of cos 100° = x = -0.1736 (approx)

☛ Also Check:

• cos 240 degrees
• cos 3 degrees
• cos 37 degrees
• cos 59 degrees
• cos 63 degrees
• cos 65 degrees

FAQs on Cos 100 Degrees

What is Cos 100 Degrees?

Cos 100 degrees is the value of cosine trigonometric function for an angle equal to 100 degrees. The value of cos 100° is -0.1736 (approx)

What is the Value of Cos 100° in Terms of Sec 100°?

Since the secant function is the reciprocal of the cosine function, we can write cos 100° as 1/sec(100°). The value of sec 100° is equal to -5.758770.

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

Using trigonometric identities, we can write cos 100° in terms of sin 100° as, cos(100°) = -√(1 - sin²(100°)). Here, the value of sin 100° is equal to 0.9848.

How to Find the Value of Cos 100 Degrees?

The value of cos 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 cos 100° is equal to the x-coordinate (-0.1736). ∴ cos 100° = -0.1736.

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

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

• ± √(1-sin²(100°))
• ± 1/√(1 + tan²(100°))
• ± cot 100°/√(1 + cot²(100°))
• ± √(cosec²(100°) - 1)/cosec 100°
• 1/sec 100°

☛ Also check: trigonometry table