Cos 330 Degrees
The value of cos 330 degrees is 0.8660254. . .. Cos 330 degrees in radians is written as cos (330° × π/180°), i.e., cos (11π/6) or cos (5.759586. . .). In this article, we will discuss the methods to find the value of cos 330 degrees with examples.
- Cos 330°: 0.8660254. . .
- Cos 330° in fraction: √3/2
- Cos (-330 degrees): 0.8660254. . .
- Cos 330° in radians: cos (11π/6) or cos (5.7595865 . . .)
What is the Value of Cos 330 Degrees?
The value of cos 330 degrees in decimal is 0.866025403. . .. Cos 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ cos 330° = cos(5.7595) = √3/2 or 0.8660254. . .
Explanation:
For cos 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 330° value = √3/2 or 0.8660254. . .
Since the cosine function is a periodic function, we can represent cos 330° as, cos 330 degrees = cos(330° + n × 360°), n ∈ Z.
⇒ cos 330° = cos 690° = cos 1050°, and so on.
Note: Since, cosine is an even function, the value of cos(-330°) = cos(330°).
Methods to Find Value of Cos 330 Degrees
The cosine function is positive in the 4th quadrant. The value of cos 330° is given as 0.86602. . .. We can find the value of cos 330 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 330 Degrees Using Unit Circle
To find the value of cos 330 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 330° angle with the positive x-axis.
- The cos of 330 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 330° = x = 0.866 (approx)
Cos 330° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 330 degrees as:
- ± √(1-sin²(330°))
- ± 1/√(1 + tan²(330°))
- ± cot 330°/√(1 + cot²(330°))
- ±√(cosec²(330°) - 1)/cosec 330°
- 1/sec 330°
Note: Since 330° lies in the 4th Quadrant, the final value of cos 330° will be positive.
We can use trigonometric identities to represent cos 330° as,
- -cos(180° - 330°) = -cos(-150°)
- -cos(180° + 330°) = -cos 510°
- sin(90° + 330°) = sin 420°
- sin(90° - 330°) = sin(-240°)
☛ Also Check:
FAQs on Cos 330 Degrees
What is Cos 330 Degrees?
Cos 330 degrees is the value of cosine trigonometric function for an angle equal to 330 degrees. The value of cos 330° is √3/2 or 0.866 (approx)
How to Find the Value of Cos 330 Degrees?
The value of cos 330 degrees can be calculated by constructing an angle of 330° 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 330° is equal to the x-coordinate (0.866). ∴ cos 330° = 0.866.
How to Find Cos 330° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 330° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(330°))
- ± 1/√(1 + tan²(330°))
- ± cot 330°/√(1 + cot²(330°))
- ± √(cosec²(330°) - 1)/cosec 330°
- 1/sec 330°
☛ Also check: trigonometry table
What is the Value of Cos 330° in Terms of Sec 330°?
Since the secant function is the reciprocal of the cosine function, we can write cos 330° as 1/sec(330°). The value of sec 330° is equal to 1.154700.
What is the Value of Cos 330 Degrees in Terms of Cot 330°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 330° can be written as -cot 330°/√(1 + cot²(330°)). Here, the value of cot 330° is equal to -1.73205.