Cos 65 Degrees

The value of cos 65 degrees is 0.4226182. . .. Cos 65 degrees in radians is written as cos (65° × π/180°), i.e., cos (13π/36) or cos (1.134464. . .). In this article, we will discuss the methods to find the value of cos 65 degrees with examples.

• Cos 65°: 0.4226182. . .
• Cos (-65 degrees): 0.4226182. . .
• Cos 65° in radians: cos (13π/36) or cos (1.1344640 . . .)

What is the Value of Cos 65 Degrees?

The value of cos 65 degrees in decimal is 0.422618261. . .. Cos 65 degrees can also be expressed using the equivalent of the given angle (65 degrees) in radians (1.13446 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 65 degrees = 65° × (π/180°) rad = 13π/36 or 1.1344 . . .
∴ cos 65° = cos(1.1344) = 0.4226182. . .

Explanation:

For cos 65 degrees, the angle 65° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 65° value = 0.4226182. . .
Since the cosine function is a periodic function, we can represent cos 65° as, cos 65 degrees = cos(65° + n × 360°), n ∈ Z.
⇒ cos 65° = cos 425° = cos 785°, and so on.
Note: Since, cosine is an even function, the value of cos(-65°) = cos(65°).

Methods to Find Value of Cos 65 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 65° is given as 0.42261. . .. We can find the value of cos 65 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 65 Degrees Using Unit Circle

To find the value of cos 65 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 65° angle with the positive x-axis.
• The cos of 65 degrees equals the x-coordinate(0.4226) of the point of intersection (0.4226, 0.9063) of unit circle and r.

Hence the value of cos 65° = x = 0.4226 (approx)

Cos 65° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 65 degrees as:

• ± √(1-sin²(65°))
• ± 1/√(1 + tan²(65°))
• ± cot 65°/√(1 + cot²(65°))
• ±√(cosec²(65°) - 1)/cosec 65°
• 1/sec 65°

Note: Since 65° lies in the 1st Quadrant, the final value of cos 65° will be positive.

We can use trigonometric identities to represent cos 65° as,

• -cos(180° - 65°) = -cos 115°
• -cos(180° + 65°) = -cos 245°
• sin(90° + 65°) = sin 155°
• sin(90° - 65°) = sin 25°

☛ Also Check:

• cos 53 degrees
• cos 2 degrees
• cos 30 degrees
• cos 245 degrees
• cos 108 degrees
• cos 99 degrees

FAQs on Cos 65 Degrees

What is Cos 65 Degrees?

Cos 65 degrees is the value of cosine trigonometric function for an angle equal to 65 degrees. The value of cos 65° is 0.4226 (approx)

How to Find the Value of Cos 65 Degrees?

The value of cos 65 degrees can be calculated by constructing an angle of 65° with the x-axis, and then finding the coordinates of the corresponding point (0.4226, 0.9063) on the unit circle. The value of cos 65° is equal to the x-coordinate (0.4226). ∴ cos 65° = 0.4226.

How to Find Cos 65° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 65° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(65°))
• ± 1/√(1 + tan²(65°))
• ± cot 65°/√(1 + cot²(65°))
• ± √(cosec²(65°) - 1)/cosec 65°
• 1/sec 65°

☛ Also check: trigonometry table

What is the Value of Cos 65° in Terms of Sec 65°?

Since the secant function is the reciprocal of the cosine function, we can write cos 65° as 1/sec(65°). The value of sec 65° is equal to 2.366201.

What is the Value of Cos 65 Degrees in Terms of Sin 65°?

Using trigonometric identities, we can write cos 65° in terms of sin 65° as, cos(65°) = √(1 - sin²(65°)). Here, the value of sin 65° is equal to 0.9063.