Cos 57 Degrees
The value of cos 57 degrees is 0.5446390. . .. Cos 57 degrees in radians is written as cos (57° × π/180°), i.e., cos (19π/60) or cos (0.994837. . .). In this article, we will discuss the methods to find the value of cos 57 degrees with examples.
- Cos 57°: 0.5446390. . .
- Cos (-57 degrees): 0.5446390. . .
- Cos 57° in radians: cos (19π/60) or cos (0.9948376 . . .)
What is the Value of Cos 57 Degrees?
The value of cos 57 degrees in decimal is 0.544639035. . .. Cos 57 degrees can also be expressed using the equivalent of the given angle (57 degrees) in radians (0.99483 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 57 degrees = 57° × (π/180°) rad = 19π/60 or 0.9948 . . .
∴ cos 57° = cos(0.9948) = 0.5446390. . .
Explanation:
For cos 57 degrees, the angle 57° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 57° value = 0.5446390. . .
Since the cosine function is a periodic function, we can represent cos 57° as, cos 57 degrees = cos(57° + n × 360°), n ∈ Z.
⇒ cos 57° = cos 417° = cos 777°, and so on.
Note: Since, cosine is an even function, the value of cos(-57°) = cos(57°).
Methods to Find Value of Cos 57 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 57° is given as 0.54463. . .. We can find the value of cos 57 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 57 Degrees Using Unit Circle
To find the value of cos 57 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 57° angle with the positive x-axis.
- The cos of 57 degrees equals the x-coordinate(0.5446) of the point of intersection (0.5446, 0.8387) of unit circle and r.
Hence the value of cos 57° = x = 0.5446 (approx)
Cos 57° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 57 degrees as:
- ± √(1-sin²(57°))
- ± 1/√(1 + tan²(57°))
- ± cot 57°/√(1 + cot²(57°))
- ±√(cosec²(57°) - 1)/cosec 57°
- 1/sec 57°
Note: Since 57° lies in the 1st Quadrant, the final value of cos 57° will be positive.
We can use trigonometric identities to represent cos 57° as,
- -cos(180° - 57°) = -cos 123°
- -cos(180° + 57°) = -cos 237°
- sin(90° + 57°) = sin 147°
- sin(90° - 57°) = sin 33°
☛ Also Check:
FAQs on Cos 57 Degrees
What is Cos 57 Degrees?
Cos 57 degrees is the value of cosine trigonometric function for an angle equal to 57 degrees. The value of cos 57° is 0.5446 (approx)
What is the Value of Cos 57 Degrees in Terms of Tan 57°?
We know, using trig identities, we can write cos 57° as 1/√(1 + tan²(57°)). Here, the value of tan 57° is equal to 1.539864.
How to Find Cos 57° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 57° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(57°))
- ± 1/√(1 + tan²(57°))
- ± cot 57°/√(1 + cot²(57°))
- ± √(cosec²(57°) - 1)/cosec 57°
- 1/sec 57°
☛ Also check: trigonometric table
What is the Value of Cos 57° in Terms of Cosec 57°?
Since the cosine function can be represented using the cosecant function, we can write cos 57° as [√(cosec²(57°) - 1)/cosec 57°]. The value of cosec 57° is equal to 1.19236.
How to Find the Value of Cos 57 Degrees?
The value of cos 57 degrees can be calculated by constructing an angle of 57° with the x-axis, and then finding the coordinates of the corresponding point (0.5446, 0.8387) on the unit circle. The value of cos 57° is equal to the x-coordinate (0.5446). ∴ cos 57° = 0.5446.