Cos 10 Degrees

The value of cos 10 degrees is 0.9848077. . .. Cos 10 degrees in radians is written as cos (10° × π/180°), i.e., cos (π/18) or cos (0.174532. . .). In this article, we will discuss the methods to find the value of cos 10 degrees with examples.

• Cos 10°: 0.9848077. . .
• Cos (-10 degrees): 0.9848077. . .
• Cos 10° in radians: cos (π/18) or cos (0.1745329 . . .)

What is the Value of Cos 10 Degrees?

The value of cos 10 degrees in decimal is 0.984807753. . .. Cos 10 degrees can also be expressed using the equivalent of the given angle (10 degrees) in radians (0.17453 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 10 degrees = 10° × (π/180°) rad = π/18 or 0.1745 . . .
∴ cos 10° = cos(0.1745) = 0.9848077. . .

Explanation:

For cos 10 degrees, the angle 10° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 10° value = 0.9848077. . .
Since the cosine function is a periodic function, we can represent cos 10° as, cos 10 degrees = cos(10° + n × 360°), n ∈ Z.
⇒ cos 10° = cos 370° = cos 730°, and so on.
Note: Since, cosine is an even function, the value of cos(-10°) = cos(10°).

Methods to Find Value of Cos 10 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 10° is given as 0.98480. . .. We can find the value of cos 10 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 10° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 10 degrees as:

• ± √(1-sin²(10°))
• ± 1/√(1 + tan²(10°))
• ± cot 10°/√(1 + cot²(10°))
• ±√(cosec²(10°) - 1)/cosec 10°
• 1/sec 10°

Note: Since 10° lies in the 1st Quadrant, the final value of cos 10° will be positive.

We can use trigonometric identities to represent cos 10° as,

• -cos(180° - 10°) = -cos 170°
• -cos(180° + 10°) = -cos 190°
• sin(90° + 10°) = sin 100°
• sin(90° - 10°) = sin 80°

Cos 10 Degrees Using Unit Circle

To find the value of cos 10 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 10° angle with the positive x-axis.
• The cos of 10 degrees equals the x-coordinate(0.9848) of the point of intersection (0.9848, 0.1736) of unit circle and r.

Hence the value of cos 10° = x = 0.9848 (approx)

☛ Also Check:

• cos 10 degrees
• cos 30 degrees
• cos 75 degrees
• cos 85 degrees
• cos 326 degrees
• cos 690 degrees

FAQs on Cos 10 Degrees

What is Cos 10 Degrees?

Cos 10 degrees is the value of cosine trigonometric function for an angle equal to 10 degrees. The value of cos 10° is 0.9848 (approx)

What is the Value of Cos 10 Degrees in Terms of Cot 10°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 10° can be written as cot 10°/√(1 + cot²(10°)). Here, the value of cot 10° is equal to 5.67128.

How to Find the Value of Cos 10 Degrees?

The value of cos 10 degrees can be calculated by constructing an angle of 10° with the x-axis, and then finding the coordinates of the corresponding point (0.9848, 0.1736) on the unit circle. The value of cos 10° is equal to the x-coordinate (0.9848). ∴ cos 10° = 0.9848.

How to Find Cos 10° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 10° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(10°))
• ± 1/√(1 + tan²(10°))
• ± cot 10°/√(1 + cot²(10°))
• ± √(cosec²(10°) - 1)/cosec 10°
• 1/sec 10°

☛ Also check: trigonometry table

What is the Exact Value of cos 10 Degrees?

The exact value of cos 10 degrees can be given accurately up to 8 decimal places as 0.98480775.