Cos 855 Degrees
The value of cos 855 degrees is -0.7071067. . .. Cos 855 degrees in radians is written as cos (855° × π/180°), i.e., cos (19π/4) or cos (14.922565. . .). In this article, we will discuss the methods to find the value of cos 855 degrees with examples.
- Cos 855°: -0.7071067. . .
- Cos 855° in fraction: −(1/√2)
- Cos (-855 degrees): -0.7071067. . .
- Cos 855° in radians: cos (19π/4) or cos (14.9225651 . . .)
What is the Value of Cos 855 Degrees?
The value of cos 855 degrees in decimal is -0.707106781. . .. Cos 855 degrees can also be expressed using the equivalent of the given angle (855 degrees) in radians (14.92256 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 855 degrees = 855° × (π/180°) rad = 19π/4 or 14.9225 . . .
∴ cos 855° = cos(14.9225) = −(1/√2) or -0.7071067. . .
Explanation:
For cos 855°, the angle 855° > 360°. Given the periodic property of the cosine function, we can represent it as cos(855° mod 360°) = cos(135°). The angle 855°, coterminal to angle 135°, is located in the Second Quadrant(Quadrant II).
Since cosine function is negative in the 2nd quadrant, thus cos 855 degrees value = −(1/√2) or -0.7071067. . .
Similarly, cos 855° can also be written as, cos 855 degrees = (855° + n × 360°), n ∈ Z.
⇒ cos 855° = cos 1215° = cos 1575°, and so on.
Note: Since, cosine is an even function, the value of cos(-855°) = cos(855°).
Methods to Find Value of Cos 855 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 855° is given as -0.70710. . .. We can find the value of cos 855 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 855 Degrees Using Unit Circle
To find the value of cos 855 degrees using the unit circle, represent 855° in the form (2 × 360°) + 135° [∵ 855°>360°] ∵ cosine is a periodic function, cos 855° = cos 135°.
- Rotate ‘r’ anticlockwise to form 135° or 855° angle with the positive x-axis.
- The cos of 855 degrees equals the x-coordinate(-0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r.
Hence the value of cos 855° = x = -0.7071 (approx)
Cos 855° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 855 degrees as:
- ± √(1-sin²(855°))
- ± 1/√(1 + tan²(855°))
- ± cot 855°/√(1 + cot²(855°))
- ±√(cosec²(855°) - 1)/cosec 855°
- 1/sec 855°
Note: Since 855° lies in the 2nd Quadrant, the final value of cos 855° will be negative.
We can use trigonometric identities to represent cos 855° as,
- -cos(180° - 855°) = -cos(-675°)
- -cos(180° + 855°) = -cos 1035°
- sin(90° + 855°) = sin 945°
- sin(90° - 855°) = sin(-765°)
☛ Also Check:
FAQs on Cos 855 Degrees
What is Cos 855 Degrees?
Cos 855 degrees is the value of cosine trigonometric function for an angle equal to 855 degrees. The value of cos 855° is −(1/√2) or -0.7071 (approx)
What is the Value of Cos 855 Degrees in Terms of Tan 855°?
We know, using trig identities, we can write cos 855° as -1/√(1 + tan²(855°)). Here, the value of tan 855° is equal to -1.
How to Find Cos 855° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 855° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(855°))
- ± 1/√(1 + tan²(855°))
- ± cot 855°/√(1 + cot²(855°))
- ± √(cosec²(855°) - 1)/cosec 855°
- 1/sec 855°
☛ Also check: trigonometry table
What is the Value of Cos 855° in Terms of Sec 855°?
Since the secant function is the reciprocal of the cosine function, we can write cos 855° as 1/sec(855°). The value of sec 855° is equal to -1.414213.
How to Find the Value of Cos 855 Degrees?
The value of cos 855 degrees can be calculated by constructing an angle of 855° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of cos 855° is equal to the x-coordinate (-0.7071). ∴ cos 855° = -0.7071.