Cos 125 Degrees
The value of cos 125 degrees is -0.5735764. . .. Cos 125 degrees in radians is written as cos (125° × π/180°), i.e., cos (25π/36) or cos (2.181661. . .). In this article, we will discuss the methods to find the value of cos 125 degrees with examples.
- Cos 125°: -0.5735764. . .
- Cos (-125 degrees): -0.5735764. . .
- Cos 125° in radians: cos (25π/36) or cos (2.1816615 . . .)
What is the Value of Cos 125 Degrees?
The value of cos 125 degrees in decimal is -0.573576436. . .. Cos 125 degrees can also be expressed using the equivalent of the given angle (125 degrees) in radians (2.18166 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 125 degrees = 125° × (π/180°) rad = 25π/36 or 2.1816 . . .
∴ cos 125° = cos(2.1816) = -0.5735764. . .
Explanation:
For cos 125 degrees, the angle 125° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 125° value = -0.5735764. . .
Since the cosine function is a periodic function, we can represent cos 125° as, cos 125 degrees = cos(125° + n × 360°), n ∈ Z.
⇒ cos 125° = cos 485° = cos 845°, and so on.
Note: Since, cosine is an even function, the value of cos(-125°) = cos(125°).
Methods to Find Value of Cos 125 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 125° is given as -0.57357. . .. We can find the value of cos 125 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 125 Degrees Using Unit Circle
To find the value of cos 125 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 125° angle with the positive x-axis.
- The cos of 125 degrees equals the x-coordinate(-0.5736) of the point of intersection (-0.5736, 0.8192) of unit circle and r.
Hence the value of cos 125° = x = -0.5736 (approx)
Cos 125° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 125 degrees as:
- ± √(1-sin²(125°))
- ± 1/√(1 + tan²(125°))
- ± cot 125°/√(1 + cot²(125°))
- ±√(cosec²(125°) - 1)/cosec 125°
- 1/sec 125°
Note: Since 125° lies in the 2nd Quadrant, the final value of cos 125° will be negative.
We can use trigonometric identities to represent cos 125° as,
- -cos(180° - 125°) = -cos 55°
- -cos(180° + 125°) = -cos 305°
- sin(90° + 125°) = sin 215°
- sin(90° - 125°) = sin(-35°)
☛ Also Check:
FAQs on Cos 125 Degrees
What is Cos 125 Degrees?
Cos 125 degrees is the value of cosine trigonometric function for an angle equal to 125 degrees. The value of cos 125° is -0.5736 (approx)
What is the Exact Value of cos 125 Degrees?
The exact value of cos 125 degrees can be given accurately up to 8 decimal places as -0.57357643.
How to Find Cos 125° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 125° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(125°))
- ± 1/√(1 + tan²(125°))
- ± cot 125°/√(1 + cot²(125°))
- ± √(cosec²(125°) - 1)/cosec 125°
- 1/sec 125°
☛ Also check: trigonometry table
How to Find the Value of Cos 125 Degrees?
The value of cos 125 degrees can be calculated by constructing an angle of 125° with the x-axis, and then finding the coordinates of the corresponding point (-0.5736, 0.8192) on the unit circle. The value of cos 125° is equal to the x-coordinate (-0.5736). ∴ cos 125° = -0.5736.
What is the Value of Cos 125 Degrees in Terms of Cot 125°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 125° can be written as cot 125°/√(1 + cot²(125°)). Here, the value of cot 125° is equal to -0.70020.