Cos 200 Degrees
The value of cos 200 degrees is -0.9396926. . .. Cos 200 degrees in radians is written as cos (200° × π/180°), i.e., cos (10π/9) or cos (3.490658. . .). In this article, we will discuss the methods to find the value of cos 200 degrees with examples.
- Cos 200°: -0.9396926. . .
- Cos (-200 degrees): -0.9396926. . .
- Cos 200° in radians: cos (10π/9) or cos (3.4906585 . . .)
What is the Value of Cos 200 Degrees?
The value of cos 200 degrees in decimal is -0.939692620. . .. Cos 200 degrees can also be expressed using the equivalent of the given angle (200 degrees) in radians (3.49065 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 200 degrees = 200° × (π/180°) rad = 10π/9 or 3.4906 . . .
∴ cos 200° = cos(3.4906) = -0.9396926. . .
Explanation:
For cos 200 degrees, the angle 200° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 200° value = -0.9396926. . .
Since the cosine function is a periodic function, we can represent cos 200° as, cos 200 degrees = cos(200° + n × 360°), n ∈ Z.
⇒ cos 200° = cos 560° = cos 920°, and so on.
Note: Since, cosine is an even function, the value of cos(-200°) = cos(200°).
Methods to Find Value of Cos 200 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 200° is given as -0.93969. . .. We can find the value of cos 200 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 200° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 200 degrees as:
- ± √(1-sin²(200°))
- ± 1/√(1 + tan²(200°))
- ± cot 200°/√(1 + cot²(200°))
- ±√(cosec²(200°) - 1)/cosec 200°
- 1/sec 200°
Note: Since 200° lies in the 3rd Quadrant, the final value of cos 200° will be negative.
We can use trigonometric identities to represent cos 200° as,
- -cos(180° - 200°) = -cos(-20°)
- -cos(180° + 200°) = -cos 380°
- sin(90° + 200°) = sin 290°
- sin(90° - 200°) = sin(-110°)
Cos 200 Degrees Using Unit Circle
To find the value of cos 200 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 200° angle with the positive x-axis.
- The cos of 200 degrees equals the x-coordinate(-0.9397) of the point of intersection (-0.9397, -0.342) of unit circle and r.
Hence the value of cos 200° = x = -0.9397 (approx)
☛ Also Check:
FAQs on Cos 200 Degrees
What is Cos 200 Degrees?
Cos 200 degrees is the value of cosine trigonometric function for an angle equal to 200 degrees. The value of cos 200° is -0.9397 (approx)
What is the Value of Cos 200 Degrees in Terms of Cot 200°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 200° can be written as -cot 200°/√(1 + cot²(200°)). Here, the value of cot 200° is equal to 2.74747.
How to Find the Value of Cos 200 Degrees?
The value of cos 200 degrees can be calculated by constructing an angle of 200° with the x-axis, and then finding the coordinates of the corresponding point (-0.9397, -0.342) on the unit circle. The value of cos 200° is equal to the x-coordinate (-0.9397). ∴ cos 200° = -0.9397.
How to Find Cos 200° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 200° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(200°))
- ± 1/√(1 + tan²(200°))
- ± cot 200°/√(1 + cot²(200°))
- ± √(cosec²(200°) - 1)/cosec 200°
- 1/sec 200°
☛ Also check: trigonometry table
What is the Value of Cos 200° in Terms of Sec 200°?
Since the secant function is the reciprocal of the cosine function, we can write cos 200° as 1/sec(200°). The value of sec 200° is equal to -1.064177.