Cos 9 Degrees

The value of cos 9 degrees is 0.9876883. . .. Cos 9 degrees in radians is written as cos (9° × π/180°), i.e., cos (π/20) or cos (0.157079. . .). In this article, we will discuss the methods to find the value of cos 9 degrees with examples.

• Cos 9°: 0.9876883. . .
• Cos (-9 degrees): 0.9876883. . .
• Cos 9° in radians: cos (π/20) or cos (0.1570796 . . .)

What is the Value of Cos 9 Degrees?

The value of cos 9 degrees in decimal is 0.987688340. . .. Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 9 degrees = 9° × (π/180°) rad = π/20 or 0.1570 . . .
∴ cos 9° = cos(0.1570) = 0.9876883. . .

Explanation:

For cos 9 degrees, the angle 9° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 9° value = 0.9876883. . .
Since the cosine function is a periodic function, we can represent cos 9° as, cos 9 degrees = cos(9° + n × 360°), n ∈ Z.
⇒ cos 9° = cos 369° = cos 729°, and so on.
Note: Since, cosine is an even function, the value of cos(-9°) = cos(9°).

Methods to Find Value of Cos 9 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 9° is given as 0.98768. . .. We can find the value of cos 9 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 9 Degrees Using Unit Circle

To find the value of cos 9 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 9° angle with the positive x-axis.
• The cos of 9 degrees equals the x-coordinate(0.9877) of the point of intersection (0.9877, 0.1564) of unit circle and r.

Hence the value of cos 9° = x = 0.9877 (approx)

Cos 9° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 9 degrees as:

• ± √(1-sin²(9°))
• ± 1/√(1 + tan²(9°))
• ± cot 9°/√(1 + cot²(9°))
• ±√(cosec²(9°) - 1)/cosec 9°
• 1/sec 9°

Note: Since 9° lies in the 1st Quadrant, the final value of cos 9° will be positive.

We can use trigonometric identities to represent cos 9° as,

• -cos(180° - 9°) = -cos 171°
• -cos(180° + 9°) = -cos 189°
• sin(90° + 9°) = sin 99°
• sin(90° - 9°) = sin 81°

☛ Also Check:

• cos 120 degrees
• cos 0 degrees
• cos 150 degrees
• cos 89 degrees
• cos 125 degrees
• cos 900 degrees

FAQs on Cos 9 Degrees

What is Cos 9 Degrees?

Cos 9 degrees is the value of cosine trigonometric function for an angle equal to 9 degrees. The value of cos 9° is 0.9877 (approx)

What is the Value of Cos 9 Degrees in Terms of Sin 9°?

Using trigonometric identities, we can write cos 9° in terms of sin 9° as, cos(9°) = √(1 - sin²(9°)). Here, the value of sin 9° is equal to 0.1564.

How to Find Cos 9° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 9° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(9°))
• ± 1/√(1 + tan²(9°))
• ± cot 9°/√(1 + cot²(9°))
• ± √(cosec²(9°) - 1)/cosec 9°
• 1/sec 9°

☛ Also check: trigonometric table

What is the Value of Cos 9° in Terms of Sec 9°?

Since the secant function is the reciprocal of the cosine function, we can write cos 9° as 1/sec(9°). The value of sec 9° is equal to 1.012465.

How to Find the Value of Cos 9 Degrees?

The value of cos 9 degrees can be calculated by constructing an angle of 9° with the x-axis, and then finding the coordinates of the corresponding point (0.9877, 0.1564) on the unit circle. The value of cos 9° is equal to the x-coordinate (0.9877). ∴ cos 9° = 0.9877.