Cos 315 Degrees
The value of cos 315 degrees is 0.7071067. . .. Cos 315 degrees in radians is written as cos (315° × π/180°), i.e., cos (7π/4) or cos (5.497787. . .). In this article, we will discuss the methods to find the value of cos 315 degrees with examples.
- Cos 315°: 0.7071067. . .
- Cos 315° in fraction: 1/√2
- Cos (-315 degrees): 0.7071067. . .
- Cos 315° in radians: cos (7π/4) or cos (5.4977871 . . .)
What is the Value of Cos 315 Degrees?
The value of cos 315 degrees in decimal is 0.707106781. . .. Cos 315 degrees can also be expressed using the equivalent of the given angle (315 degrees) in radians (5.49778 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 315 degrees = 315° × (π/180°) rad = 7π/4 or 5.4977 . . .
∴ cos 315° = cos(5.4977) = 1/√2 or 0.7071067. . .
Explanation:
For cos 315 degrees, the angle 315° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 315° value = 1/√2 or 0.7071067. . .
Since the cosine function is a periodic function, we can represent cos 315° as, cos 315 degrees = cos(315° + n × 360°), n ∈ Z.
⇒ cos 315° = cos 675° = cos 1035°, and so on.
Note: Since, cosine is an even function, the value of cos(-315°) = cos(315°).
Methods to Find Value of Cos 315 Degrees
The cosine function is positive in the 4th quadrant. The value of cos 315° is given as 0.70710. . .. We can find the value of cos 315 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 315 Degrees Using Unit Circle
To find the value of cos 315 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 315° angle with the positive x-axis.
- The cos of 315 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 315° = x = 0.7071 (approx)
Cos 315° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 315 degrees as:
- ± √(1-sin²(315°))
- ± 1/√(1 + tan²(315°))
- ± cot 315°/√(1 + cot²(315°))
- ±√(cosec²(315°) - 1)/cosec 315°
- 1/sec 315°
Note: Since 315° lies in the 4th Quadrant, the final value of cos 315° will be positive.
We can use trigonometric identities to represent cos 315° as,
- -cos(180° - 315°) = -cos(-135°)
- -cos(180° + 315°) = -cos 495°
- sin(90° + 315°) = sin 405°
- sin(90° - 315°) = sin(-225°)
☛ Also Check:
FAQs on Cos 315 Degrees
What is Cos 315 Degrees?
Cos 315 degrees is the value of cosine trigonometric function for an angle equal to 315 degrees. The value of cos 315° is 1/√2 or 0.7071 (approx)
What is the Value of Cos 315° in Terms of Cosec 315°?
Since the cosine function can be represented using the cosecant function, we can write cos 315° as -[√(cosec²(315°) - 1)/cosec 315°]. The value of cosec 315° is equal to -1.41421.
How to Find Cos 315° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 315° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(315°))
- ± 1/√(1 + tan²(315°))
- ± cot 315°/√(1 + cot²(315°))
- ± √(cosec²(315°) - 1)/cosec 315°
- 1/sec 315°
☛ Also check: trigonometry table
What is the Value of Cos 315 Degrees in Terms of Tan 315°?
We know, using trig identities, we can write cos 315° as 1/√(1 + tan²(315°)). Here, the value of tan 315° is equal to -1.
How to Find the Value of Cos 315 Degrees?
The value of cos 315 degrees can be calculated by constructing an angle of 315° 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 315° is equal to the x-coordinate (0.7071). ∴ cos 315° = 0.7071.