Cos 99 Degrees

The value of cos 99 degrees is -0.1564344. . .. Cos 99 degrees in radians is written as cos (99° × π/180°), i.e., cos (11π/20) or cos (1.727875. . .). In this article, we will discuss the methods to find the value of cos 99 degrees with examples.

• Cos 99°: -0.1564344. . .
• Cos (-99 degrees): -0.1564344. . .
• Cos 99° in radians: cos (11π/20) or cos (1.7278759 . . .)

What is the Value of Cos 99 Degrees?

The value of cos 99 degrees in decimal is -0.156434465. . .. Cos 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 . . .
∴ cos 99° = cos(1.7278) = -0.1564344. . .

Explanation:

For cos 99 degrees, the angle 99° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 99° value = -0.1564344. . .
Since the cosine function is a periodic function, we can represent cos 99° as, cos 99 degrees = cos(99° + n × 360°), n ∈ Z.
⇒ cos 99° = cos 459° = cos 819°, and so on.
Note: Since, cosine is an even function, the value of cos(-99°) = cos(99°).

Methods to Find Value of Cos 99 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 99° is given as -0.15643. . .. We can find the value of cos 99 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 99° in Terms of Trigonometric Functions

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

• ± √(1-sin²(99°))
• ± 1/√(1 + tan²(99°))
• ± cot 99°/√(1 + cot²(99°))
• ±√(cosec²(99°) - 1)/cosec 99°
• 1/sec 99°

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

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

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

Cos 99 Degrees Using Unit Circle

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

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

Hence the value of cos 99° = x = -0.1564 (approx)

☛ Also Check:

• cos 20 degrees
• cos 75 degrees
• cos 300 degrees
• cos 61 degrees
• cos 126 degrees
• cos 54 degrees

FAQs on Cos 99 Degrees

What is Cos 99 Degrees?

Cos 99 degrees is the value of cosine trigonometric function for an angle equal to 99 degrees. The value of cos 99° is -0.1564 (approx)

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

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

What is the Value of Cos 99° in Terms of Sec 99°?

Since the secant function is the reciprocal of the cosine function, we can write cos 99° as 1/sec(99°). The value of sec 99° is equal to -6.392453.

How to Find the Value of Cos 99 Degrees?

The value of cos 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 cos 99° is equal to the x-coordinate (-0.1564). ∴ cos 99° = -0.1564.

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

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

• ± √(1-sin²(99°))
• ± 1/√(1 + tan²(99°))
• ± cot 99°/√(1 + cot²(99°))
• ± √(cosec²(99°) - 1)/cosec 99°
• 1/sec 99°

☛ Also check: trigonometric table