Cos 24 Degrees
The value of cos 24 degrees is 0.9135454. . .. Cos 24 degrees in radians is written as cos (24° × π/180°), i.e., cos (2π/15) or cos (0.418879. . .). In this article, we will discuss the methods to find the value of cos 24 degrees with examples.
- Cos 24°: 0.9135454. . .
- Cos (-24 degrees): 0.9135454. . .
- Cos 24° in radians: cos (2π/15) or cos (0.4188790 . . .)
What is the Value of Cos 24 Degrees?
The value of cos 24 degrees in decimal is 0.913545457. . .. Cos 24 degrees can also be expressed using the equivalent of the given angle (24 degrees) in radians (0.41887 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 24 degrees = 24° × (π/180°) rad = 2π/15 or 0.4188 . . .
∴ cos 24° = cos(0.4188) = 0.9135454. . .
Explanation:
For cos 24 degrees, the angle 24° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 24° value = 0.9135454. . .
Since the cosine function is a periodic function, we can represent cos 24° as, cos 24 degrees = cos(24° + n × 360°), n ∈ Z.
⇒ cos 24° = cos 384° = cos 744°, and so on.
Note: Since, cosine is an even function, the value of cos(-24°) = cos(24°).
Methods to Find Value of Cos 24 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 24° is given as 0.91354. . .. We can find the value of cos 24 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 24° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 24 degrees as:
- ± √(1-sin²(24°))
- ± 1/√(1 + tan²(24°))
- ± cot 24°/√(1 + cot²(24°))
- ±√(cosec²(24°) - 1)/cosec 24°
- 1/sec 24°
Note: Since 24° lies in the 1st Quadrant, the final value of cos 24° will be positive.
We can use trigonometric identities to represent cos 24° as,
- -cos(180° - 24°) = -cos 156°
- -cos(180° + 24°) = -cos 204°
- sin(90° + 24°) = sin 114°
- sin(90° - 24°) = sin 66°
Cos 24 Degrees Using Unit Circle
To find the value of cos 24 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 24° angle with the positive x-axis.
- The cos of 24 degrees equals the x-coordinate(0.9135) of the point of intersection (0.9135, 0.4067) of unit circle and r.
Hence the value of cos 24° = x = 0.9135 (approx)
☛ Also Check:
FAQs on Cos 24 Degrees
What is Cos 24 Degrees?
Cos 24 degrees is the value of cosine trigonometric function for an angle equal to 24 degrees. The value of cos 24° is 0.9135 (approx)
How to Find the Value of Cos 24 Degrees?
The value of cos 24 degrees can be calculated by constructing an angle of 24° with the x-axis, and then finding the coordinates of the corresponding point (0.9135, 0.4067) on the unit circle. The value of cos 24° is equal to the x-coordinate (0.9135). ∴ cos 24° = 0.9135.
What is the Exact Value of cos 24 Degrees?
The exact value of cos 24 degrees can be given accurately up to 8 decimal places as 0.91354545.
What is the Value of Cos 24 Degrees in Terms of Cot 24°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 24° can be written as cot 24°/√(1 + cot²(24°)). Here, the value of cot 24° is equal to 2.24603.
How to Find Cos 24° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 24° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(24°))
- ± 1/√(1 + tan²(24°))
- ± cot 24°/√(1 + cot²(24°))
- ± √(cosec²(24°) - 1)/cosec 24°
- 1/sec 24°
☛ Also check: trigonometry table