Cos 130 Degrees
The value of cos 130 degrees is -0.6427876. . .. Cos 130 degrees in radians is written as cos (130° × π/180°), i.e., cos (13π/18) or cos (2.268928. . .). In this article, we will discuss the methods to find the value of cos 130 degrees with examples.
- Cos 130°: -0.6427876. . .
- Cos (-130 degrees): -0.6427876. . .
- Cos 130° in radians: cos (13π/18) or cos (2.2689280 . . .)
What is the Value of Cos 130 Degrees?
The value of cos 130 degrees in decimal is -0.642787609. . .. Cos 130 degrees can also be expressed using the equivalent of the given angle (130 degrees) in radians (2.26892 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 130 degrees = 130° × (π/180°) rad = 13π/18 or 2.2689 . . .
∴ cos 130° = cos(2.2689) = -0.6427876. . .
Explanation:
For cos 130 degrees, the angle 130° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 130° value = -0.6427876. . .
Since the cosine function is a periodic function, we can represent cos 130° as, cos 130 degrees = cos(130° + n × 360°), n ∈ Z.
⇒ cos 130° = cos 490° = cos 850°, and so on.
Note: Since, cosine is an even function, the value of cos(-130°) = cos(130°).
Methods to Find Value of Cos 130 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 130° is given as -0.64278. . .. We can find the value of cos 130 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 130 Degrees Using Unit Circle
To find the value of cos 130 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 130° angle with the positive x-axis.
- The cos of 130 degrees equals the x-coordinate(-0.6428) of the point of intersection (-0.6428, 0.766) of unit circle and r.
Hence the value of cos 130° = x = -0.6428 (approx)
Cos 130° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 130 degrees as:
- ± √(1-sin²(130°))
- ± 1/√(1 + tan²(130°))
- ± cot 130°/√(1 + cot²(130°))
- ±√(cosec²(130°) - 1)/cosec 130°
- 1/sec 130°
Note: Since 130° lies in the 2nd Quadrant, the final value of cos 130° will be negative.
We can use trigonometric identities to represent cos 130° as,
- -cos(180° - 130°) = -cos 50°
- -cos(180° + 130°) = -cos 310°
- sin(90° + 130°) = sin 220°
- sin(90° - 130°) = sin(-40°)
☛ Also Check:
FAQs on Cos 130 Degrees
What is Cos 130 Degrees?
Cos 130 degrees is the value of cosine trigonometric function for an angle equal to 130 degrees. The value of cos 130° is -0.6428 (approx)
How to Find Cos 130° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 130° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(130°))
- ± 1/√(1 + tan²(130°))
- ± cot 130°/√(1 + cot²(130°))
- ± √(cosec²(130°) - 1)/cosec 130°
- 1/sec 130°
☛ Also check: trigonometry table
How to Find the Value of Cos 130 Degrees?
The value of cos 130 degrees can be calculated by constructing an angle of 130° with the x-axis, and then finding the coordinates of the corresponding point (-0.6428, 0.766) on the unit circle. The value of cos 130° is equal to the x-coordinate (-0.6428). ∴ cos 130° = -0.6428.
What is the Value of Cos 130 Degrees in Terms of Cot 130°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 130° can be written as cot 130°/√(1 + cot²(130°)). Here, the value of cot 130° is equal to -0.83909.
What is the Value of Cos 130° in Terms of Cosec 130°?
Since the cosine function can be represented using the cosecant function, we can write cos 130° as -[√(cosec²(130°) - 1)/cosec 130°]. The value of cosec 130° is equal to 1.30540.