Cos 195 Degrees
The value of cos 195 degrees is -0.9659258. . .. Cos 195 degrees in radians is written as cos (195° × π/180°), i.e., cos (13π/12) or cos (3.403392. . .). In this article, we will discuss the methods to find the value of cos 195 degrees with examples.
- Cos 195°: -0.9659258. . .
- Cos 195° in fraction: -(√6+√2)/4
- Cos (-195 degrees): -0.9659258. . .
- Cos 195° in radians: cos (13π/12) or cos (3.4033920 . . .)
What is the Value of Cos 195 Degrees?
The value of cos 195 degrees in decimal is -0.965925826. . .. Cos 195 degrees can also be expressed using the equivalent of the given angle (195 degrees) in radians (3.40339 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 195 degrees = 195° × (π/180°) rad = 13π/12 or 3.4033 . . .
∴ cos 195° = cos(3.4033) = -(√6+√2)/4 or -0.9659258. . .
Explanation:
For cos 195 degrees, the angle 195° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 195° value = -(√6+√2)/4 or -0.9659258. . .
Since the cosine function is a periodic function, we can represent cos 195° as, cos 195 degrees = cos(195° + n × 360°), n ∈ Z.
⇒ cos 195° = cos 555° = cos 915°, and so on.
Note: Since, cosine is an even function, the value of cos(-195°) = cos(195°).
Methods to Find Value of Cos 195 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 195° is given as -0.96592. . .. We can find the value of cos 195 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 195° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 195 degrees as:
- ± √(1-sin²(195°))
- ± 1/√(1 + tan²(195°))
- ± cot 195°/√(1 + cot²(195°))
- ±√(cosec²(195°) - 1)/cosec 195°
- 1/sec 195°
Note: Since 195° lies in the 3rd Quadrant, the final value of cos 195° will be negative.
We can use trigonometric identities to represent cos 195° as,
- -cos(180° - 195°) = -cos(-15°)
- -cos(180° + 195°) = -cos 375°
- sin(90° + 195°) = sin 285°
- sin(90° - 195°) = sin(-105°)
Cos 195 Degrees Using Unit Circle
To find the value of cos 195 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 195° angle with the positive x-axis.
- The cos of 195 degrees equals the x-coordinate(-0.9659) of the point of intersection (-0.9659, -0.2588) of unit circle and r.
Hence the value of cos 195° = x = -0.9659 (approx)
☛ Also Check:
FAQs on Cos 195 Degrees
What is Cos 195 Degrees?
Cos 195 degrees is the value of cosine trigonometric function for an angle equal to 195 degrees. The value of cos 195° is -(√6+√2)/4 or -0.9659 (approx)
What is the Value of Cos 195 Degrees in Terms of Sin 195°?
Using trigonometric identities, we can write cos 195° in terms of sin 195° as, cos(195°) = -√(1 - sin²(195°)). Here, the value of sin 195° is equal to -(√6 - √2)/4.
What is the Value of Cos 195° in Terms of Sec 195°?
Since the secant function is the reciprocal of the cosine function, we can write cos 195° as 1/sec(195°). The value of sec 195° is equal to -1.035276.
How to Find Cos 195° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 195° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(195°))
- ± 1/√(1 + tan²(195°))
- ± cot 195°/√(1 + cot²(195°))
- ± √(cosec²(195°) - 1)/cosec 195°
- 1/sec 195°
☛ Also check: trigonometric table
How to Find the Value of Cos 195 Degrees?
The value of cos 195 degrees can be calculated by constructing an angle of 195° with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, -0.2588) on the unit circle. The value of cos 195° is equal to the x-coordinate (-0.9659). ∴ cos 195° = -0.9659.