Cos 225 Degrees
The value of cos 225 degrees is -0.7071067. . .. Cos 225 degrees in radians is written as cos (225° × π/180°), i.e., cos (5π/4) or cos (3.926990. . .). In this article, we will discuss the methods to find the value of cos 225 degrees with examples.
- Cos 225°: -0.7071067. . .
- Cos 225° in fraction: -(1/√2)
- Cos (-225 degrees): -0.7071067. . .
- Cos 225° in radians: cos (5π/4) or cos (3.9269908 . . .)
What is the Value of Cos 225 Degrees?
The value of cos 225 degrees in decimal is -0.707106781. . .. Cos 225 degrees can also be expressed using the equivalent of the given angle (225 degrees) in radians (3.92699 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 225 degrees = 225° × (π/180°) rad = 5π/4 or 3.9269 . . .
∴ cos 225° = cos(3.9269) = -(1/√2) or -0.7071067. . .
Explanation:
For cos 225 degrees, the angle 225° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 225° value = -(1/√2) or -0.7071067. . .
Since the cosine function is a periodic function, we can represent cos 225° as, cos 225 degrees = cos(225° + n × 360°), n ∈ Z.
⇒ cos 225° = cos 585° = cos 945°, and so on.
Note: Since, cosine is an even function, the value of cos(-225°) = cos(225°).
Methods to Find Value of Cos 225 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 225° is given as -0.70710. . .. We can find the value of cos 225 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 225 Degrees Using Unit Circle
To find the value of cos 225 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 225° angle with the positive x-axis.
- The cos of 225 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 225° = x = -0.7071 (approx)
Cos 225° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 225 degrees as:
- ± √(1-sin²(225°))
- ± 1/√(1 + tan²(225°))
- ± cot 225°/√(1 + cot²(225°))
- ±√(cosec²(225°) - 1)/cosec 225°
- 1/sec 225°
Note: Since 225° lies in the 3rd Quadrant, the final value of cos 225° will be negative.
We can use trigonometric identities to represent cos 225° as,
- -cos(180° - 225°) = -cos(-45°)
- -cos(180° + 225°) = -cos 405°
- sin(90° + 225°) = sin 315°
- sin(90° - 225°) = sin(-135°)
☛ Also Check:
FAQs on Cos 225 Degrees
What is Cos 225 Degrees?
Cos 225 degrees is the value of cosine trigonometric function for an angle equal to 225 degrees. The value of cos 225° is -(1/√2) or -0.7071 (approx)
What is the Value of Cos 225° in Terms of Sec 225°?
Since the secant function is the reciprocal of the cosine function, we can write cos 225° as 1/sec(225°). The value of sec 225° is equal to -1.414213.
How to Find the Value of Cos 225 Degrees?
The value of cos 225 degrees can be calculated by constructing an angle of 225° 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 225° is equal to the x-coordinate (-0.7071). ∴ cos 225° = -0.7071.
How to Find Cos 225° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 225° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(225°))
- ± 1/√(1 + tan²(225°))
- ± cot 225°/√(1 + cot²(225°))
- ± √(cosec²(225°) - 1)/cosec 225°
- 1/sec 225°
☛ Also check: trigonometry table
What is the Value of Cos 225 Degrees in Terms of Cot 225°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 225° can be written as -cot 225°/√(1 + cot²(225°)). Here, the value of cot 225° is equal to 1.