Cos 13 Degrees

The value of cos 13 degrees is 0.9743700. . .. Cos 13 degrees in radians is written as cos (13° × π/180°), i.e., cos (0.226892. . .). In this article, we will discuss the methods to find the value of cos 13 degrees with examples.

• Cos 13°: 0.9743700. . .
• Cos (-13 degrees): 0.9743700. . .
• Cos 13° in radians: cos (0.2268928 . . .)

What is the Value of Cos 13 Degrees?

The value of cos 13 degrees in decimal is 0.974370064. . .. Cos 13 degrees can also be expressed using the equivalent of the given angle (13 degrees) in radians (0.22689 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 13 degrees = 13° × (π/180°) rad = 0.2268 . . .
∴ cos 13° = cos(0.2268) = 0.9743700. . .

Explanation:

For cos 13 degrees, the angle 13° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 13° value = 0.9743700. . .
Since the cosine function is a periodic function, we can represent cos 13° as, cos 13 degrees = cos(13° + n × 360°), n ∈ Z.
⇒ cos 13° = cos 373° = cos 733°, and so on.
Note: Since, cosine is an even function, the value of cos(-13°) = cos(13°).

Methods to Find Value of Cos 13 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 13° is given as 0.97437. . .. We can find the value of cos 13 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 13° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 13 degrees as:

• ± √(1-sin²(13°))
• ± 1/√(1 + tan²(13°))
• ± cot 13°/√(1 + cot²(13°))
• ±√(cosec²(13°) - 1)/cosec 13°
• 1/sec 13°

Note: Since 13° lies in the 1st Quadrant, the final value of cos 13° will be positive.

We can use trigonometric identities to represent cos 13° as,

• -cos(180° - 13°) = -cos 167°
• -cos(180° + 13°) = -cos 193°
• sin(90° + 13°) = sin 103°
• sin(90° - 13°) = sin 77°

Cos 13 Degrees Using Unit Circle

To find the value of cos 13 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 13° angle with the positive x-axis.
• The cos of 13 degrees equals the x-coordinate(0.9744) of the point of intersection (0.9744, 0.225) of unit circle and r.

Hence the value of cos 13° = x = 0.9744 (approx)

☛ Also Check:

• cos 20 degrees
• cos 3 degrees
• cos 37 degrees
• cos 65 degrees
• cos 345 degrees
• cos 780 degrees

FAQs on Cos 13 Degrees

What is Cos 13 Degrees?

Cos 13 degrees is the value of cosine trigonometric function for an angle equal to 13 degrees. The value of cos 13° is 0.9744 (approx)

How to Find Cos 13° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 13° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(13°))
• ± 1/√(1 + tan²(13°))
• ± cot 13°/√(1 + cot²(13°))
• ± √(cosec²(13°) - 1)/cosec 13°
• 1/sec 13°

☛ Also check: trigonometric table

What is the Value of Cos 13 Degrees in Terms of Sin 13°?

Using trigonometric identities, we can write cos 13° in terms of sin 13° as, cos(13°) = √(1 - sin²(13°)). Here, the value of sin 13° is equal to 0.225.

How to Find the Value of Cos 13 Degrees?

The value of cos 13 degrees can be calculated by constructing an angle of 13° with the x-axis, and then finding the coordinates of the corresponding point (0.9744, 0.225) on the unit circle. The value of cos 13° is equal to the x-coordinate (0.9744). ∴ cos 13° = 0.9744.

What is the Exact Value of cos 13 Degrees?

The exact value of cos 13 degrees can be given accurately up to 8 decimal places as 0.97437006.