Cos 930 Degrees
The value of cos 930 degrees is -0.8660254. . .. Cos 930 degrees in radians is written as cos (930° × π/180°), i.e., cos (31π/6) or cos (16.231562. . .). In this article, we will discuss the methods to find the value of cos 930 degrees with examples.
- Cos 930°: -0.8660254. . .
- Cos 930° in fraction: -√(3)/2
- Cos (-930 degrees): -0.8660254. . .
- Cos 930° in radians: cos (31π/6) or cos (16.2315620 . . .)
What is the Value of Cos 930 Degrees?
The value of cos 930 degrees in decimal is -0.866025403. . .. Cos 930 degrees can also be expressed using the equivalent of the given angle (930 degrees) in radians (16.23156 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 930 degrees = 930° × (π/180°) rad = 31π/6 or 16.2315 . . .
∴ cos 930° = cos(16.2315) = -√(3)/2 or -0.8660254. . .
Explanation:
For cos 930°, the angle 930° > 360°. Given the periodic property of the cosine function, we can represent it as cos(930° mod 360°) = cos(210°). The angle 930°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since cosine function is negative in the 3rd quadrant, thus cos 930 degrees value = -√(3)/2 or -0.8660254. . .
Similarly, cos 930° can also be written as, cos 930 degrees = (930° + n × 360°), n ∈ Z.
⇒ cos 930° = cos 1290° = cos 1650°, and so on.
Note: Since, cosine is an even function, the value of cos(-930°) = cos(930°).
Methods to Find Value of Cos 930 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 930° is given as -0.86602. . .. We can find the value of cos 930 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 930 Degrees Using Unit Circle
To find the value of cos 930 degrees using the unit circle, represent 930° in the form (2 × 360°) + 210° [∵ 930°>360°] ∵ cosine is a periodic function, cos 930° = cos 210°.
- Rotate ‘r’ anticlockwise to form 210° or 930° angle with the positive x-axis.
- The cos of 930 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 930° = x = -0.866 (approx)
Cos 930° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 930 degrees as:
- ± √(1-sin²(930°))
- ± 1/√(1 + tan²(930°))
- ± cot 930°/√(1 + cot²(930°))
- ±√(cosec²(930°) - 1)/cosec 930°
- 1/sec 930°
Note: Since 930° lies in the 3rd Quadrant, the final value of cos 930° will be negative.
We can use trigonometric identities to represent cos 930° as,
- -cos(180° - 930°) = -cos(-750°)
- -cos(180° + 930°) = -cos 1110°
- sin(90° + 930°) = sin 1020°
- sin(90° - 930°) = sin(-840°)
☛ Also Check:
FAQs on Cos 930 Degrees
What is Cos 930 Degrees?
Cos 930 degrees is the value of cosine trigonometric function for an angle equal to 930 degrees. The value of cos 930° is -√(3)/2 or -0.866 (approx)
What is the Value of Cos 930 Degrees in Terms of Tan 930°?
We know, using trig identities, we can write cos 930° as -1/√(1 + tan²(930°)). Here, the value of tan 930° is equal to 0.577350.
What is the Value of Cos 930° in Terms of Cosec 930°?
Since the cosine function can be represented using the cosecant function, we can write cos 930° as [√(cosec²(930°) - 1)/cosec 930°]. The value of cosec 930° is equal to -2.
How to Find the Value of Cos 930 Degrees?
The value of cos 930 degrees can be calculated by constructing an angle of 930° 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 930° is equal to the x-coordinate (-0.866). ∴ cos 930° = -0.866.
How to Find Cos 930° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 930° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(930°))
- ± 1/√(1 + tan²(930°))
- ± cot 930°/√(1 + cot²(930°))
- ± √(cosec²(930°) - 1)/cosec 930°
- 1/sec 930°
☛ Also check: trigonometric table