Cos 20 Degrees

The value of cos 20 degrees is 0.9396926. . .. Cos 20 degrees in radians is written as cos (20° × π/180°), i.e., cos (π/9) or cos (0.349065. . .). In this article, we will discuss the methods to find the value of cos 20 degrees with examples.

• Cos 20°: 0.9396926. . .
• Cos (-20 degrees): 0.9396926. . .
• Cos 20° in radians: cos (π/9) or cos (0.3490658 . . .)

What is the Value of Cos 20 Degrees?

The value of cos 20 degrees in decimal is 0.939692620. . .. Cos 20 degrees can also be expressed using the equivalent of the given angle (20 degrees) in radians (0.34906 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 20 degrees = 20° × (π/180°) rad = π/9 or 0.3490 . . .
∴ cos 20° = cos(0.3490) = 0.9396926. . .

Explanation:

For cos 20 degrees, the angle 20° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 20° value = 0.9396926. . .
Since the cosine function is a periodic function, we can represent cos 20° as, cos 20 degrees = cos(20° + n × 360°), n ∈ Z.
⇒ cos 20° = cos 380° = cos 740°, and so on.
Note: Since, cosine is an even function, the value of cos(-20°) = cos(20°).

Methods to Find Value of Cos 20 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 20° is given as 0.93969. . .. We can find the value of cos 20 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 20° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 20 degrees as:

• ± √(1-sin²(20°))
• ± 1/√(1 + tan²(20°))
• ± cot 20°/√(1 + cot²(20°))
• ±√(cosec²(20°) - 1)/cosec 20°
• 1/sec 20°

Note: Since 20° lies in the 1st Quadrant, the final value of cos 20° will be positive.

We can use trigonometric identities to represent cos 20° as,

• -cos(180° - 20°) = -cos 160°
• -cos(180° + 20°) = -cos 200°
• sin(90° + 20°) = sin 110°
• sin(90° - 20°) = sin 70°

Cos 20 Degrees Using Unit Circle

To find the value of cos 20 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 20° angle with the positive x-axis.
• The cos of 20 degrees equals the x-coordinate(0.9397) of the point of intersection (0.9397, 0.342) of unit circle and r.

Hence the value of cos 20° = x = 0.9397 (approx)

☛ Also Check:

• cos 15 degrees
• cos 37 degrees
• cos 90 degrees
• cos 1170 degrees
• cos 69 degrees
• cos 16 degrees

FAQs on Cos 20 Degrees

What is Cos 20 Degrees?

Cos 20 degrees is the value of cosine trigonometric function for an angle equal to 20 degrees. The value of cos 20° is 0.9397 (approx)

What is the Value of Cos 20 Degrees in Terms of Cot 20°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 20° can be written as cot 20°/√(1 + cot²(20°)). Here, the value of cot 20° is equal to 2.74747.

What is the Exact Value of cos 20 Degrees?

The exact value of cos 20 degrees can be given accurately up to 8 decimal places as 0.93969262.

How to Find the Value of Cos 20 Degrees?

The value of cos 20 degrees can be calculated by constructing an angle of 20° with the x-axis, and then finding the coordinates of the corresponding point (0.9397, 0.342) on the unit circle. The value of cos 20° is equal to the x-coordinate (0.9397). ∴ cos 20° = 0.9397.

How to Find Cos 20° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 20° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(20°))
• ± 1/√(1 + tan²(20°))
• ± cot 20°/√(1 + cot²(20°))
• ± √(cosec²(20°) - 1)/cosec 20°
• 1/sec 20°

☛ Also check: trigonometry table