Cos 63 Degrees

The value of cos 63 degrees is 0.4539904. . .. Cos 63 degrees in radians is written as cos (63° × π/180°), i.e., cos (7π/20) or cos (1.099557. . .). In this article, we will discuss the methods to find the value of cos 63 degrees with examples.

• Cos 63°: 0.4539904. . .
• Cos (-63 degrees): 0.4539904. . .
• Cos 63° in radians: cos (7π/20) or cos (1.0995574 . . .)

What is the Value of Cos 63 Degrees?

The value of cos 63 degrees in decimal is 0.453990499. . .. Cos 63 degrees can also be expressed using the equivalent of the given angle (63 degrees) in radians (1.09955 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 63 degrees = 63° × (π/180°) rad = 7π/20 or 1.0995 . . .
∴ cos 63° = cos(1.0995) = 0.4539904. . .

Explanation:

For cos 63 degrees, the angle 63° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 63° value = 0.4539904. . .
Since the cosine function is a periodic function, we can represent cos 63° as, cos 63 degrees = cos(63° + n × 360°), n ∈ Z.
⇒ cos 63° = cos 423° = cos 783°, and so on.
Note: Since, cosine is an even function, the value of cos(-63°) = cos(63°).

Methods to Find Value of Cos 63 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 63° is given as 0.45399. . .. We can find the value of cos 63 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 63° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 63 degrees as:

• ± √(1-sin²(63°))
• ± 1/√(1 + tan²(63°))
• ± cot 63°/√(1 + cot²(63°))
• ±√(cosec²(63°) - 1)/cosec 63°
• 1/sec 63°

Note: Since 63° lies in the 1st Quadrant, the final value of cos 63° will be positive.

We can use trigonometric identities to represent cos 63° as,

• -cos(180° - 63°) = -cos 117°
• -cos(180° + 63°) = -cos 243°
• sin(90° + 63°) = sin 153°
• sin(90° - 63°) = sin 27°

Cos 63 Degrees Using Unit Circle

To find the value of cos 63 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 63° angle with the positive x-axis.
• The cos of 63 degrees equals the x-coordinate(0.454) of the point of intersection (0.454, 0.891) of unit circle and r.

Hence the value of cos 63° = x = 0.454 (approx)

☛ Also Check:

• cos 18 degrees
• cos 150 degrees
• cos 75 degrees
• cos 100 degrees
• cos 81 degrees
• cos 17 degrees

FAQs on Cos 63 Degrees

What is Cos 63 Degrees?

Cos 63 degrees is the value of cosine trigonometric function for an angle equal to 63 degrees. The value of cos 63° is 0.454 (approx)

How to Find Cos 63° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 63° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(63°))
• ± 1/√(1 + tan²(63°))
• ± cot 63°/√(1 + cot²(63°))
• ± √(cosec²(63°) - 1)/cosec 63°
• 1/sec 63°

☛ Also check: trigonometry table

What is the Exact Value of cos 63 Degrees?

The exact value of cos 63 degrees can be given accurately up to 8 decimal places as 0.45399049.

How to Find the Value of Cos 63 Degrees?

The value of cos 63 degrees can be calculated by constructing an angle of 63° with the x-axis, and then finding the coordinates of the corresponding point (0.454, 0.891) on the unit circle. The value of cos 63° is equal to the x-coordinate (0.454). ∴ cos 63° = 0.454.

What is the Value of Cos 63 Degrees in Terms of Cot 63°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 63° can be written as cot 63°/√(1 + cot²(63°)). Here, the value of cot 63° is equal to 0.50952.