Cos 660 Degrees
The value of cos 660 degrees is 0.5. Cos 660 degrees in radians is written as cos (660° × π/180°), i.e., cos (11π/3) or cos (11.519173. . .). In this article, we will discuss the methods to find the value of cos 660 degrees with examples.
- Cos 660°: 0.5
- Cos 660° in fraction: 1/2
- Cos (-660 degrees): 0.5
- Cos 660° in radians: cos (11π/3) or cos (11.5191730 . . .)
What is the Value of Cos 660 Degrees?
The value of cos 660 degrees in decimal is 0.5. Cos 660 degrees can also be expressed using the equivalent of the given angle (660 degrees) in radians (11.51917 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 660 degrees = 660° × (π/180°) rad = 11π/3 or 11.5191 . . .
∴ cos 660° = cos(11.5191) = 1/2 or 0.5
Explanation:
For cos 660°, the angle 660° > 360°. Given the periodic property of the cosine function, we can represent it as cos(660° mod 360°) = cos(300°). The angle 660°, coterminal to angle 300°, is located in the Fourth Quadrant(Quadrant IV).
Since cosine function is positive in the 4th quadrant, thus cos 660 degrees value = 1/2 or 0.5
Similarly, cos 660° can also be written as, cos 660 degrees = (660° + n × 360°), n ∈ Z.
⇒ cos 660° = cos 1020° = cos 1380°, and so on.
Note: Since, cosine is an even function, the value of cos(-660°) = cos(660°).
Methods to Find Value of Cos 660 Degrees
The cosine function is positive in the 4th quadrant. The value of cos 660° is given as 0.5. We can find the value of cos 660 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 660 Degrees Using Unit Circle
To find the value of cos 660 degrees using the unit circle, represent 660° in the form (1 × 360°) + 300° [∵ 660°>360°] ∵ cosine is a periodic function, cos 660° = cos 300°.
- Rotate ‘r’ anticlockwise to form 300° or 660° angle with the positive x-axis.
- The cos of 660 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 660° = x = 0.5
Cos 660° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 660 degrees as:
- ± √(1-sin²(660°))
- ± 1/√(1 + tan²(660°))
- ± cot 660°/√(1 + cot²(660°))
- ±√(cosec²(660°) - 1)/cosec 660°
- 1/sec 660°
Note: Since 660° lies in the 4th Quadrant, the final value of cos 660° will be positive.
We can use trigonometric identities to represent cos 660° as,
- -cos(180° - 660°) = -cos(-480°)
- -cos(180° + 660°) = -cos 840°
- sin(90° + 660°) = sin 750°
- sin(90° - 660°) = sin(-570°)
☛ Also Check:
FAQs on Cos 660 Degrees
What is Cos 660 Degrees?
Cos 660 degrees is the value of cosine trigonometric function for an angle equal to 660 degrees. The value of cos 660° is 1/2 or 0.5
How to Find the Value of Cos 660 Degrees?
The value of cos 660 degrees can be calculated by constructing an angle of 660° 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 660° is equal to the x-coordinate (0.5). ∴ cos 660° = 0.5.
What is the Value of Cos 660° in Terms of Cosec 660°?
Since the cosine function can be represented using the cosecant function, we can write cos 660° as -[√(cosec²(660°) - 1)/cosec 660°]. The value of cosec 660° is equal to -1.15470.
What is the Value of Cos 660 Degrees in Terms of Tan 660°?
We know, using trig identities, we can write cos 660° as 1/√(1 + tan²(660°)). Here, the value of tan 660° is equal to -1.732050.
How to Find Cos 660° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 660° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(660°))
- ± 1/√(1 + tan²(660°))
- ± cot 660°/√(1 + cot²(660°))
- ± √(cosec²(660°) - 1)/cosec 660°
- 1/sec 660°
☛ Also check: trigonometry table