Cos 64 Degrees

The value of cos 64 degrees is 0.4383711. . .. Cos 64 degrees in radians is written as cos (64° × π/180°), i.e., cos (16π/45) or cos (1.117010. . .). In this article, we will discuss the methods to find the value of cos 64 degrees with examples.

• Cos 64°: 0.4383711. . .
• Cos (-64 degrees): 0.4383711. . .
• Cos 64° in radians: cos (16π/45) or cos (1.1170107 . . .)

What is the Value of Cos 64 Degrees?

The value of cos 64 degrees in decimal is 0.438371146. . .. Cos 64 degrees can also be expressed using the equivalent of the given angle (64 degrees) in radians (1.11701 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 64 degrees = 64° × (π/180°) rad = 16π/45 or 1.1170 . . .
∴ cos 64° = cos(1.1170) = 0.4383711. . .

Explanation:

For cos 64 degrees, the angle 64° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 64° value = 0.4383711. . .
Since the cosine function is a periodic function, we can represent cos 64° as, cos 64 degrees = cos(64° + n × 360°), n ∈ Z.
⇒ cos 64° = cos 424° = cos 784°, and so on.
Note: Since, cosine is an even function, the value of cos(-64°) = cos(64°).

Methods to Find Value of Cos 64 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 64° is given as 0.43837. . .. We can find the value of cos 64 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 64 Degrees Using Unit Circle

To find the value of cos 64 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 64° angle with the positive x-axis.
• The cos of 64 degrees equals the x-coordinate(0.4384) of the point of intersection (0.4384, 0.8988) of unit circle and r.

Hence the value of cos 64° = x = 0.4384 (approx)

Cos 64° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 64 degrees as:

• ± √(1-sin²(64°))
• ± 1/√(1 + tan²(64°))
• ± cot 64°/√(1 + cot²(64°))
• ±√(cosec²(64°) - 1)/cosec 64°
• 1/sec 64°

Note: Since 64° lies in the 1st Quadrant, the final value of cos 64° will be positive.

We can use trigonometric identities to represent cos 64° as,

• -cos(180° - 64°) = -cos 116°
• -cos(180° + 64°) = -cos 244°
• sin(90° + 64°) = sin 154°
• sin(90° - 64°) = sin 26°

☛ Also Check:

• cos 10 degrees
• cos 2 degrees
• cos 225 degrees
• cos 74 degrees
• cos 48 degrees
• cos 570 degrees

FAQs on Cos 64 Degrees

What is Cos 64 Degrees?

Cos 64 degrees is the value of cosine trigonometric function for an angle equal to 64 degrees. The value of cos 64° is 0.4384 (approx)

What is the Value of Cos 64° in Terms of Cosec 64°?

Since the cosine function can be represented using the cosecant function, we can write cos 64° as [√(cosec²(64°) - 1)/cosec 64°]. The value of cosec 64° is equal to 1.11260.

How to Find Cos 64° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 64° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(64°))
• ± 1/√(1 + tan²(64°))
• ± cot 64°/√(1 + cot²(64°))
• ± √(cosec²(64°) - 1)/cosec 64°
• 1/sec 64°

☛ Also check: trigonometric table

What is the Value of Cos 64 Degrees in Terms of Cot 64°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 64° can be written as cot 64°/√(1 + cot²(64°)). Here, the value of cot 64° is equal to 0.48773.

How to Find the Value of Cos 64 Degrees?

The value of cos 64 degrees can be calculated by constructing an angle of 64° with the x-axis, and then finding the coordinates of the corresponding point (0.4384, 0.8988) on the unit circle. The value of cos 64° is equal to the x-coordinate (0.4384). ∴ cos 64° = 0.4384.