Cos 3 Degrees
The value of cos 3 degrees is 0.9986295. . .. Cos 3 degrees in radians is written as cos (3° × π/180°), i.e., cos (π/60) or cos (0.052359. . .). In this article, we will discuss the methods to find the value of cos 3 degrees with examples.
- Cos 3°: 0.9986295. . .
- Cos (-3 degrees): 0.9986295. . .
- Cos 3° in radians: cos (π/60) or cos (0.0523598 . . .)
What is the Value of Cos 3 Degrees?
The value of cos 3 degrees in decimal is 0.998629534. . .. Cos 3 degrees can also be expressed using the equivalent of the given angle (3 degrees) in radians (0.05235 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 3 degrees = 3° × (π/180°) rad = π/60 or 0.0523 . . .
∴ cos 3° = cos(0.0523) = 0.9986295. . .
Explanation:
For cos 3 degrees, the angle 3° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 3° value = 0.9986295. . .
Since the cosine function is a periodic function, we can represent cos 3° as, cos 3 degrees = cos(3° + n × 360°), n ∈ Z.
⇒ cos 3° = cos 363° = cos 723°, and so on.
Note: Since, cosine is an even function, the value of cos(-3°) = cos(3°).
Methods to Find Value of Cos 3 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 3° is given as 0.99862. . .. We can find the value of cos 3 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 3 Degrees Using Unit Circle
To find the value of cos 3 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 3° angle with the positive x-axis.
- The cos of 3 degrees equals the x-coordinate(0.9986) of the point of intersection (0.9986, 0.0523) of unit circle and r.
Hence the value of cos 3° = x = 0.9986 (approx)
Cos 3° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 3 degrees as:
- ± √(1-sin²(3°))
- ± 1/√(1 + tan²(3°))
- ± cot 3°/√(1 + cot²(3°))
- ±√(cosec²(3°) - 1)/cosec 3°
- 1/sec 3°
Note: Since 3° lies in the 1st Quadrant, the final value of cos 3° will be positive.
We can use trigonometric identities to represent cos 3° as,
- -cos(180° - 3°) = -cos 177°
- -cos(180° + 3°) = -cos 183°
- sin(90° + 3°) = sin 93°
- sin(90° - 3°) = sin 87°
☛ Also Check:
FAQs on Cos 3 Degrees
What is Cos 3 Degrees?
Cos 3 degrees is the value of cosine trigonometric function for an angle equal to 3 degrees. The value of cos 3° is 0.9986 (approx)
What is the Exact Value of cos 3 Degrees?
The exact value of cos 3 degrees can be given accurately up to 8 decimal places as 0.99862953.
How to Find the Value of Cos 3 Degrees?
The value of cos 3 degrees can be calculated by constructing an angle of 3° with the x-axis, and then finding the coordinates of the corresponding point (0.9986, 0.0523) on the unit circle. The value of cos 3° is equal to the x-coordinate (0.9986). ∴ cos 3° = 0.9986.
What is the Value of Cos 3 Degrees in Terms of Tan 3°?
We know, using trig identities, we can write cos 3° as 1/√(1 + tan²(3°)). Here, the value of tan 3° is equal to 0.052407.
How to Find Cos 3° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 3° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(3°))
- ± 1/√(1 + tan²(3°))
- ± cot 3°/√(1 + cot²(3°))
- ± √(cosec²(3°) - 1)/cosec 3°
- 1/sec 3°
☛ Also check: trigonometric table