Cos 840 Degrees
The value of cos 840 degrees is -0.5. Cos 840 degrees in radians is written as cos (840° × π/180°), i.e., cos (14π/3) or cos (14.660765. . .). In this article, we will discuss the methods to find the value of cos 840 degrees with examples.
- Cos 840°: -0.5
- Cos 840° in fraction: -(1/2)
- Cos (-840 degrees): -0.5
- Cos 840° in radians: cos (14π/3) or cos (14.6607657 . . .)
What is the Value of Cos 840 Degrees?
The value of cos 840 degrees in decimal is -0.5. Cos 840 degrees can also be expressed using the equivalent of the given angle (840 degrees) in radians (14.66076 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 840 degrees = 840° × (π/180°) rad = 14π/3 or 14.6607 . . .
∴ cos 840° = cos(14.6607) = -(1/2) or -0.5
Explanation:
For cos 840°, the angle 840° > 360°. Given the periodic property of the cosine function, we can represent it as cos(840° mod 360°) = cos(120°). The angle 840°, coterminal to angle 120°, is located in the Second Quadrant(Quadrant II).
Since cosine function is negative in the 2nd quadrant, thus cos 840 degrees value = -(1/2) or -0.5
Similarly, cos 840° can also be written as, cos 840 degrees = (840° + n × 360°), n ∈ Z.
⇒ cos 840° = cos 1200° = cos 1560°, and so on.
Note: Since, cosine is an even function, the value of cos(-840°) = cos(840°).
Methods to Find Value of Cos 840 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 840° is given as -0.5. We can find the value of cos 840 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 840° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 840 degrees as:
- ± √(1-sin²(840°))
- ± 1/√(1 + tan²(840°))
- ± cot 840°/√(1 + cot²(840°))
- ±√(cosec²(840°) - 1)/cosec 840°
- 1/sec 840°
Note: Since 840° lies in the 2nd Quadrant, the final value of cos 840° will be negative.
We can use trigonometric identities to represent cos 840° as,
- -cos(180° - 840°) = -cos(-660°)
- -cos(180° + 840°) = -cos 1020°
- sin(90° + 840°) = sin 930°
- sin(90° - 840°) = sin(-750°)
Cos 840 Degrees Using Unit Circle
To find the value of cos 840 degrees using the unit circle, represent 840° in the form (2 × 360°) + 120° [∵ 840°>360°] ∵ cosine is a periodic function, cos 840° = cos 120°.
- Rotate ‘r’ anticlockwise to form 120° or 840° angle with the positive x-axis.
- The cos of 840 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 840° = x = -0.5
☛ Also Check:
FAQs on Cos 840 Degrees
What is Cos 840 Degrees?
Cos 840 degrees is the value of cosine trigonometric function for an angle equal to 840 degrees. The value of cos 840° is -(1/2) or -0.5
How to Find the Value of Cos 840 Degrees?
The value of cos 840 degrees can be calculated by constructing an angle of 840° 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 840° is equal to the x-coordinate (-0.5). ∴ cos 840° = -0.5.
What is the Value of Cos 840 Degrees in Terms of Cot 840°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 840° can be written as cot 840°/√(1 + cot²(840°)). Here, the value of cot 840° is equal to -0.57735.
How to Find Cos 840° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 840° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(840°))
- ± 1/√(1 + tan²(840°))
- ± cot 840°/√(1 + cot²(840°))
- ± √(cosec²(840°) - 1)/cosec 840°
- 1/sec 840°
☛ Also check: trigonometric table
What is the Value of Cos 840° in Terms of Sec 840°?
Since the secant function is the reciprocal of the cosine function, we can write cos 840° as 1/sec(840°). The value of sec 840° is equal to -2.