Cos 600 Degrees
The value of cos 600 degrees is -0.5. Cos 600 degrees in radians is written as cos (600° × π/180°), i.e., cos (10π/3) or cos (10.471975. . .). In this article, we will discuss the methods to find the value of cos 600 degrees with examples.
- Cos 600°: -0.5
- Cos 600° in fraction: -(1/2)
- Cos (-600 degrees): -0.5
- Cos 600° in radians: cos (10π/3) or cos (10.4719755 . . .)
What is the Value of Cos 600 Degrees?
The value of cos 600 degrees in decimal is -0.5. Cos 600 degrees can also be expressed using the equivalent of the given angle (600 degrees) in radians (10.47197 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 600 degrees = 600° × (π/180°) rad = 10π/3 or 10.4719 . . .
∴ cos 600° = cos(10.4719) = -(1/2) or -0.5
Explanation:
For cos 600°, the angle 600° > 360°. Given the periodic property of the cosine function, we can represent it as cos(600° mod 360°) = cos(240°). The angle 600°, coterminal to angle 240°, is located in the Third Quadrant(Quadrant III).
Since cosine function is negative in the 3rd quadrant, thus cos 600 degrees value = -(1/2) or -0.5
Similarly, cos 600° can also be written as, cos 600 degrees = (600° + n × 360°), n ∈ Z.
⇒ cos 600° = cos 960° = cos 1320°, and so on.
Note: Since, cosine is an even function, the value of cos(-600°) = cos(600°).
Methods to Find Value of Cos 600 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 600° is given as -0.5. We can find the value of cos 600 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 600 Degrees Using Unit Circle
To find the value of cos 600 degrees using the unit circle, represent 600° in the form (1 × 360°) + 240° [∵ 600°>360°] ∵ cosine is a periodic function, cos 600° = cos 240°.
- Rotate ‘r’ anticlockwise to form 240° or 600° angle with the positive x-axis.
- The cos of 600 degrees equals the x-coordinate(-0.5) of the point of intersection (-0.5, -0.866) of unit circle and r.
Hence the value of cos 600° = x = -0.5
Cos 600° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 600 degrees as:
- ± √(1-sin²(600°))
- ± 1/√(1 + tan²(600°))
- ± cot 600°/√(1 + cot²(600°))
- ±√(cosec²(600°) - 1)/cosec 600°
- 1/sec 600°
Note: Since 600° lies in the 3rd Quadrant, the final value of cos 600° will be negative.
We can use trigonometric identities to represent cos 600° as,
- -cos(180° - 600°) = -cos(-420°)
- -cos(180° + 600°) = -cos 780°
- sin(90° + 600°) = sin 690°
- sin(90° - 600°) = sin(-510°)
☛ Also Check:
FAQs on Cos 600 Degrees
What is Cos 600 Degrees?
Cos 600 degrees is the value of cosine trigonometric function for an angle equal to 600 degrees. The value of cos 600° is -(1/2) or -0.5
What is the Value of Cos 600 Degrees in Terms of Tan 600°?
We know, using trig identities, we can write cos 600° as -1/√(1 + tan²(600°)). Here, the value of tan 600° is equal to 1.732050.
How to Find Cos 600° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 600° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(600°))
- ± 1/√(1 + tan²(600°))
- ± cot 600°/√(1 + cot²(600°))
- ± √(cosec²(600°) - 1)/cosec 600°
- 1/sec 600°
☛ Also check: trigonometry table
What is the Value of Cos 600° in Terms of Sec 600°?
Since the secant function is the reciprocal of the cosine function, we can write cos 600° as 1/sec(600°). The value of sec 600° is equal to -2.
How to Find the Value of Cos 600 Degrees?
The value of cos 600 degrees can be calculated by constructing an angle of 600° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of cos 600° is equal to the x-coordinate (-0.5). ∴ cos 600° = -0.5.