Cos 510 Degrees
The value of cos 510 degrees is -0.8660254. . .. Cos 510 degrees in radians is written as cos (510° × π/180°), i.e., cos (17π/6) or cos (8.901179. . .). In this article, we will discuss the methods to find the value of cos 510 degrees with examples.
- Cos 510°: -0.8660254. . .
- Cos 510° in fraction: −√3/2
- Cos (-510 degrees): -0.8660254. . .
- Cos 510° in radians: cos (17π/6) or cos (8.9011791 . . .)
What is the Value of Cos 510 Degrees?
The value of cos 510 degrees in decimal is -0.866025403. . .. Cos 510 degrees can also be expressed using the equivalent of the given angle (510 degrees) in radians (8.90117 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 510 degrees = 510° × (π/180°) rad = 17π/6 or 8.9011 . . .
∴ cos 510° = cos(8.9011) = −√3/2 or -0.8660254. . .
Explanation:
For cos 510°, the angle 510° > 360°. Given the periodic property of the cosine function, we can represent it as cos(510° mod 360°) = cos(150°). The angle 510°, coterminal to angle 150°, is located in the Second Quadrant(Quadrant II).
Since cosine function is negative in the 2nd quadrant, thus cos 510 degrees value = −√3/2 or -0.8660254. . .
Similarly, cos 510° can also be written as, cos 510 degrees = (510° + n × 360°), n ∈ Z.
⇒ cos 510° = cos 870° = cos 1230°, and so on.
Note: Since, cosine is an even function, the value of cos(-510°) = cos(510°).
Methods to Find Value of Cos 510 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 510° is given as -0.86602. . .. We can find the value of cos 510 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 510 Degrees Using Unit Circle
To find the value of cos 510 degrees using the unit circle, represent 510° in the form (1 × 360°) + 150° [∵ 510°>360°] ∵ cosine is a periodic function, cos 510° = cos 150°.
- Rotate ‘r’ anticlockwise to form 150° or 510° angle with the positive x-axis.
- The cos of 510 degrees equals the x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.
Hence the value of cos 510° = x = -0.866 (approx)
Cos 510° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 510 degrees as:
- ± √(1-sin²(510°))
- ± 1/√(1 + tan²(510°))
- ± cot 510°/√(1 + cot²(510°))
- ±√(cosec²(510°) - 1)/cosec 510°
- 1/sec 510°
Note: Since 510° lies in the 2nd Quadrant, the final value of cos 510° will be negative.
We can use trigonometric identities to represent cos 510° as,
- -cos(180° - 510°) = -cos(-330°)
- -cos(180° + 510°) = -cos 690°
- sin(90° + 510°) = sin 600°
- sin(90° - 510°) = sin(-420°)
☛ Also Check:
FAQs on Cos 510 Degrees
What is Cos 510 Degrees?
Cos 510 degrees is the value of cosine trigonometric function for an angle equal to 510 degrees. The value of cos 510° is −√3/2 or -0.866 (approx)
How to Find the Value of Cos 510 Degrees?
The value of cos 510 degrees can be calculated by constructing an angle of 510° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of cos 510° is equal to the x-coordinate (-0.866). ∴ cos 510° = -0.866.
How to Find Cos 510° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 510° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(510°))
- ± 1/√(1 + tan²(510°))
- ± cot 510°/√(1 + cot²(510°))
- ± √(cosec²(510°) - 1)/cosec 510°
- 1/sec 510°
☛ Also check: trigonometry table
What is the Value of Cos 510° in Terms of Cosec 510°?
Since the cosine function can be represented using the cosecant function, we can write cos 510° as -[√(cosec²(510°) - 1)/cosec 510°]. The value of cosec 510° is equal to 2.
What is the Value of Cos 510 Degrees in Terms of Sin 510°?
Using trigonometric identities, we can write cos 510° in terms of sin 510° as, cos(510°) = -√(1 - sin²(510°)). Here, the value of sin 510° is equal to 0.5.