Cos 5 Degrees

The value of cos 5 degrees is 0.9961946. . .. Cos 5 degrees in radians is written as cos (5° × π/180°), i.e., cos (π/36) or cos (0.087266. . .). In this article, we will discuss the methods to find the value of cos 5 degrees with examples.

• Cos 5°: 0.9961946. . .
• Cos (-5 degrees): 0.9961946. . .
• Cos 5° in radians: cos (π/36) or cos (0.0872664 . . .)

What is the Value of Cos 5 Degrees?

The value of cos 5 degrees in decimal is 0.996194698. . .. Cos 5 degrees can also be expressed using the equivalent of the given angle (5 degrees) in radians (0.08726 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 5 degrees = 5° × (π/180°) rad = π/36 or 0.0872 . . .
∴ cos 5° = cos(0.0872) = 0.9961946. . .

Explanation:

For cos 5 degrees, the angle 5° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 5° value = 0.9961946. . .
Since the cosine function is a periodic function, we can represent cos 5° as, cos 5 degrees = cos(5° + n × 360°), n ∈ Z.
⇒ cos 5° = cos 365° = cos 725°, and so on.
Note: Since, cosine is an even function, the value of cos(-5°) = cos(5°).

Methods to Find Value of Cos 5 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 5° is given as 0.99619. . .. We can find the value of cos 5 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 5° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 5 degrees as:

• ± √(1-sin²(5°))
• ± 1/√(1 + tan²(5°))
• ± cot 5°/√(1 + cot²(5°))
• ±√(cosec²(5°) - 1)/cosec 5°
• 1/sec 5°

Note: Since 5° lies in the 1st Quadrant, the final value of cos 5° will be positive.

We can use trigonometric identities to represent cos 5° as,

• -cos(180° - 5°) = -cos 175°
• -cos(180° + 5°) = -cos 185°
• sin(90° + 5°) = sin 95°
• sin(90° - 5°) = sin 85°

Cos 5 Degrees Using Unit Circle

To find the value of cos 5 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 5° angle with the positive x-axis.
• The cos of 5 degrees equals the x-coordinate(0.9962) of the point of intersection (0.9962, 0.0872) of unit circle and r.

Hence the value of cos 5° = x = 0.9962 (approx)

☛ Also Check:

• cos 0 degrees
• cos 11 degrees
• cos 90 degrees
• cos 19 degrees
• cos 85 degrees
• cos 8 degrees

FAQs on Cos 5 Degrees

What is Cos 5 Degrees?

Cos 5 degrees is the value of cosine trigonometric function for an angle equal to 5 degrees. The value of cos 5° is 0.9962 (approx)

What is the Value of Cos 5° in Terms of Sec 5°?

Since the secant function is the reciprocal of the cosine function, we can write cos 5° as 1/sec(5°). The value of sec 5° is equal to 1.003819.

How to Find Cos 5° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 5° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(5°))
• ± 1/√(1 + tan²(5°))
• ± cot 5°/√(1 + cot²(5°))
• ± √(cosec²(5°) - 1)/cosec 5°
• 1/sec 5°

☛ Also check: trigonometry table

What is the Value of Cos 5 Degrees in Terms of Tan 5°?

We know, using trig identities, we can write cos 5° as 1/√(1 + tan²(5°)). Here, the value of tan 5° is equal to 0.087488.

How to Find the Value of Cos 5 Degrees?

The value of cos 5 degrees can be calculated by constructing an angle of 5° with the x-axis, and then finding the coordinates of the corresponding point (0.9962, 0.0872) on the unit circle. The value of cos 5° is equal to the x-coordinate (0.9962). ∴ cos 5° = 0.9962.