Cos 22 Degrees

The value of cos 22 degrees is 0.9271838. . .. Cos 22 degrees in radians is written as cos (22° × π/180°), i.e., cos (11π/90) or cos (0.383972. . .). In this article, we will discuss the methods to find the value of cos 22 degrees with examples.

• Cos 22°: 0.9271838. . .
• Cos (-22 degrees): 0.9271838. . .
• Cos 22° in radians: cos (11π/90) or cos (0.3839724 . . .)

What is the Value of Cos 22 Degrees?

The value of cos 22 degrees in decimal is 0.927183854. . .. Cos 22 degrees can also be expressed using the equivalent of the given angle (22 degrees) in radians (0.38397 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 22 degrees = 22° × (π/180°) rad = 11π/90 or 0.3839 . . .
∴ cos 22° = cos(0.3839) = 0.9271838. . .

Explanation:

For cos 22 degrees, the angle 22° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 22° value = 0.9271838. . .
Since the cosine function is a periodic function, we can represent cos 22° as, cos 22 degrees = cos(22° + n × 360°), n ∈ Z.
⇒ cos 22° = cos 382° = cos 742°, and so on.
Note: Since, cosine is an even function, the value of cos(-22°) = cos(22°).

Methods to Find Value of Cos 22 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 22° is given as 0.92718. . .. We can find the value of cos 22 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 22 Degrees Using Unit Circle

To find the value of cos 22 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 22° angle with the positive x-axis.
• The cos of 22 degrees equals the x-coordinate(0.9272) of the point of intersection (0.9272, 0.3746) of unit circle and r.

Hence the value of cos 22° = x = 0.9272 (approx)

Cos 22° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 22 degrees as:

• ± √(1-sin²(22°))
• ± 1/√(1 + tan²(22°))
• ± cot 22°/√(1 + cot²(22°))
• ±√(cosec²(22°) - 1)/cosec 22°
• 1/sec 22°

Note: Since 22° lies in the 1st Quadrant, the final value of cos 22° will be positive.

We can use trigonometric identities to represent cos 22° as,

• -cos(180° - 22°) = -cos 158°
• -cos(180° + 22°) = -cos 202°
• sin(90° + 22°) = sin 112°
• sin(90° - 22°) = sin 68°

☛ Also Check:

• cos 225 degrees
• cos 180 degrees
• cos 150 degrees
• cos 47 degrees
• cos 54 degrees
• cos 74 degrees

FAQs on Cos 22 Degrees

What is Cos 22 Degrees?

Cos 22 degrees is the value of cosine trigonometric function for an angle equal to 22 degrees. The value of cos 22° is 0.9272 (approx)

How to Find Cos 22° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 22° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(22°))
• ± 1/√(1 + tan²(22°))
• ± cot 22°/√(1 + cot²(22°))
• ± √(cosec²(22°) - 1)/cosec 22°
• 1/sec 22°

☛ Also check: trigonometry table

How to Find the Value of Cos 22 Degrees?

The value of cos 22 degrees can be calculated by constructing an angle of 22° with the x-axis, and then finding the coordinates of the corresponding point (0.9272, 0.3746) on the unit circle. The value of cos 22° is equal to the x-coordinate (0.9272). ∴ cos 22° = 0.9272.

What is the Value of Cos 22° in Terms of Cosec 22°?

Since the cosine function can be represented using the cosecant function, we can write cos 22° as [√(cosec²(22°) - 1)/cosec 22°]. The value of cosec 22° is equal to 2.66946.

What is the Value of Cos 22 Degrees in Terms of Cot 22°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 22° can be written as cot 22°/√(1 + cot²(22°)). Here, the value of cot 22° is equal to 2.47508.