Cos 21 Degrees
The value of cos 21 degrees is 0.9335804. . .. Cos 21 degrees in radians is written as cos (21° × π/180°), i.e., cos (7π/60) or cos (0.366519. . .). In this article, we will discuss the methods to find the value of cos 21 degrees with examples.
- Cos 21°: 0.9335804. . .
- Cos (-21 degrees): 0.9335804. . .
- Cos 21° in radians: cos (7π/60) or cos (0.3665191 . . .)
What is the Value of Cos 21 Degrees?
The value of cos 21 degrees in decimal is 0.933580426. . .. Cos 21 degrees can also be expressed using the equivalent of the given angle (21 degrees) in radians (0.36651 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 21 degrees = 21° × (π/180°) rad = 7π/60 or 0.3665 . . .
∴ cos 21° = cos(0.3665) = 0.9335804. . .
Explanation:
For cos 21 degrees, the angle 21° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 21° value = 0.9335804. . .
Since the cosine function is a periodic function, we can represent cos 21° as, cos 21 degrees = cos(21° + n × 360°), n ∈ Z.
⇒ cos 21° = cos 381° = cos 741°, and so on.
Note: Since, cosine is an even function, the value of cos(-21°) = cos(21°).
Methods to Find Value of Cos 21 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 21° is given as 0.93358. . .. We can find the value of cos 21 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 21 Degrees Using Unit Circle
To find the value of cos 21 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 21° angle with the positive x-axis.
- The cos of 21 degrees equals the x-coordinate(0.9336) of the point of intersection (0.9336, 0.3584) of unit circle and r.
Hence the value of cos 21° = x = 0.9336 (approx)
Cos 21° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 21 degrees as:
- ± √(1-sin²(21°))
- ± 1/√(1 + tan²(21°))
- ± cot 21°/√(1 + cot²(21°))
- ±√(cosec²(21°) - 1)/cosec 21°
- 1/sec 21°
Note: Since 21° lies in the 1st Quadrant, the final value of cos 21° will be positive.
We can use trigonometric identities to represent cos 21° as,
- -cos(180° - 21°) = -cos 159°
- -cos(180° + 21°) = -cos 201°
- sin(90° + 21°) = sin 111°
- sin(90° - 21°) = sin 69°
☛ Also Check:
FAQs on Cos 21 Degrees
What is Cos 21 Degrees?
Cos 21 degrees is the value of cosine trigonometric function for an angle equal to 21 degrees. The value of cos 21° is 0.9336 (approx)
What is the Exact Value of cos 21 Degrees?
The exact value of cos 21 degrees can be given accurately up to 8 decimal places as 0.93358042.
How to Find Cos 21° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 21° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(21°))
- ± 1/√(1 + tan²(21°))
- ± cot 21°/√(1 + cot²(21°))
- ± √(cosec²(21°) - 1)/cosec 21°
- 1/sec 21°
☛ Also check: trigonometry table
How to Find the Value of Cos 21 Degrees?
The value of cos 21 degrees can be calculated by constructing an angle of 21° with the x-axis, and then finding the coordinates of the corresponding point (0.9336, 0.3584) on the unit circle. The value of cos 21° is equal to the x-coordinate (0.9336). ∴ cos 21° = 0.9336.
What is the Value of Cos 21 Degrees in Terms of Sin 21°?
Using trigonometric identities, we can write cos 21° in terms of sin 21° as, cos(21°) = √(1 - sin²(21°)). Here, the value of sin 21° is equal to 0.3584.