Cos 135 Degrees
The value of cos 135 degrees is -0.7071067. . .. Cos 135 degrees in radians is written as cos (135° × π/180°), i.e., cos (3π/4) or cos (2.356194. . .). In this article, we will discuss the methods to find the value of cos 135 degrees with examples.
- Cos 135°: -0.7071067. . .
- Cos 135° in fraction: −(1/√2)
- Cos (-135 degrees): -0.7071067. . .
- Cos 135° in radians: cos (3π/4) or cos (2.3561944 . . .)
What is the Value of Cos 135 Degrees?
The value of cos 135 degrees in decimal is -0.707106781. . .. Cos 135 degrees can also be expressed using the equivalent of the given angle (135 degrees) in radians (2.35619 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 135 degrees = 135° × (π/180°) rad = 3π/4 or 2.3561 . . .
∴ cos 135° = cos(2.3561) = −(1/√2) or -0.7071067. . .
Explanation:
For cos 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 135° value = −(1/√2) or -0.7071067. . .
Since the cosine function is a periodic function, we can represent cos 135° as, cos 135 degrees = cos(135° + n × 360°), n ∈ Z.
⇒ cos 135° = cos 495° = cos 855°, and so on.
Note: Since, cosine is an even function, the value of cos(-135°) = cos(135°).
Methods to Find Value of Cos 135 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 135° is given as -0.70710. . .. We can find the value of cos 135 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 135 Degrees Using Unit Circle
To find the value of cos 135 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis.
- The cos of 135 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 135° = x = -0.7071 (approx)
Cos 135° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 135 degrees as:
- ± √(1-sin²(135°))
- ± 1/√(1 + tan²(135°))
- ± cot 135°/√(1 + cot²(135°))
- ±√(cosec²(135°) - 1)/cosec 135°
- 1/sec 135°
Note: Since 135° lies in the 2nd Quadrant, the final value of cos 135° will be negative.
We can use trigonometric identities to represent cos 135° as,
- -cos(180° - 135°) = -cos 45°
- -cos(180° + 135°) = -cos 315°
- sin(90° + 135°) = sin 225°
- sin(90° - 135°) = sin(-45°)
☛ Also Check:
FAQs on Cos 135 Degrees
What is Cos 135 Degrees?
Cos 135 degrees is the value of cosine trigonometric function for an angle equal to 135 degrees. The value of cos 135° is −(1/√2) or -0.7071 (approx)
How to Find Cos 135° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 135° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(135°))
- ± 1/√(1 + tan²(135°))
- ± cot 135°/√(1 + cot²(135°))
- ± √(cosec²(135°) - 1)/cosec 135°
- 1/sec 135°
☛ Also check: trigonometric table
How to Find the Value of Cos 135 Degrees?
The value of cos 135 degrees can be calculated by constructing an angle of 135° 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 135° is equal to the x-coordinate (-0.7071). ∴ cos 135° = -0.7071.
What is the Value of Cos 135 Degrees in Terms of Sin 135°?
Using trigonometric identities, we can write cos 135° in terms of sin 135° as, cos(135°) = -√(1 - sin²(135°)). Here, the value of sin 135° is equal to 1/√2.
What is the Value of Cos 135° in Terms of Cosec 135°?
Since the cosine function can be represented using the cosecant function, we can write cos 135° as -[√(cosec²(135°) - 1)/cosec 135°]. The value of cosec 135° is equal to 1.41421.