Cos 23 Degrees

The value of cos 23 degrees is 0.9205048. . .. Cos 23 degrees in radians is written as cos (23° × π/180°), i.e., cos (0.401425. . .). In this article, we will discuss the methods to find the value of cos 23 degrees with examples.

• Cos 23°: 0.9205048. . .
• Cos (-23 degrees): 0.9205048. . .
• Cos 23° in radians: cos (0.4014257 . . .)

What is the Value of Cos 23 Degrees?

The value of cos 23 degrees in decimal is 0.920504853. . .. Cos 23 degrees can also be expressed using the equivalent of the given angle (23 degrees) in radians (0.40142 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 23 degrees = 23° × (π/180°) rad = 0.4014 . . .
∴ cos 23° = cos(0.4014) = 0.9205048. . .

Explanation:

For cos 23 degrees, the angle 23° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 23° value = 0.9205048. . .
Since the cosine function is a periodic function, we can represent cos 23° as, cos 23 degrees = cos(23° + n × 360°), n ∈ Z.
⇒ cos 23° = cos 383° = cos 743°, and so on.
Note: Since, cosine is an even function, the value of cos(-23°) = cos(23°).

Methods to Find Value of Cos 23 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 23° is given as 0.92050. . .. We can find the value of cos 23 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 23° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 23 degrees as:

• ± √(1-sin²(23°))
• ± 1/√(1 + tan²(23°))
• ± cot 23°/√(1 + cot²(23°))
• ±√(cosec²(23°) - 1)/cosec 23°
• 1/sec 23°

Note: Since 23° lies in the 1st Quadrant, the final value of cos 23° will be positive.

We can use trigonometric identities to represent cos 23° as,

• -cos(180° - 23°) = -cos 157°
• -cos(180° + 23°) = -cos 203°
• sin(90° + 23°) = sin 113°
• sin(90° - 23°) = sin 67°

Cos 23 Degrees Using Unit Circle

To find the value of cos 23 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 23° angle with the positive x-axis.
• The cos of 23 degrees equals the x-coordinate(0.9205) of the point of intersection (0.9205, 0.3907) of unit circle and r.

Hence the value of cos 23° = x = 0.9205 (approx)

☛ Also Check:

• cos 240 degrees
• cos 1 degrees
• cos 45 degrees
• cos 38 degrees
• cos 13 degrees
• cos 41 degrees

FAQs on Cos 23 Degrees

What is Cos 23 Degrees?

Cos 23 degrees is the value of cosine trigonometric function for an angle equal to 23 degrees. The value of cos 23° is 0.9205 (approx)

What is the Value of Cos 23 Degrees in Terms of Sin 23°?

Using trigonometric identities, we can write cos 23° in terms of sin 23° as, cos(23°) = √(1 - sin²(23°)). Here, the value of sin 23° is equal to 0.3907.

How to Find Cos 23° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 23° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(23°))
• ± 1/√(1 + tan²(23°))
• ± cot 23°/√(1 + cot²(23°))
• ± √(cosec²(23°) - 1)/cosec 23°
• 1/sec 23°

☛ Also check: trigonometric table

What is the Value of Cos 23° in Terms of Sec 23°?

Since the secant function is the reciprocal of the cosine function, we can write cos 23° as 1/sec(23°). The value of sec 23° is equal to 1.086360.

How to Find the Value of Cos 23 Degrees?

The value of cos 23 degrees can be calculated by constructing an angle of 23° with the x-axis, and then finding the coordinates of the corresponding point (0.9205, 0.3907) on the unit circle. The value of cos 23° is equal to the x-coordinate (0.9205). ∴ cos 23° = 0.9205.