Cos 1125 Degrees
The value of cos 1125 degrees is 0.7071067. . .. Cos 1125 degrees in radians is written as cos (1125° × π/180°), i.e., cos (25π/4) or cos (19.634954. . .). In this article, we will discuss the methods to find the value of cos 1125 degrees with examples.
- Cos 1125°: 0.7071067. . .
- Cos 1125° in fraction: 1/√2
- Cos (-1125 degrees): 0.7071067. . .
- Cos 1125° in radians: cos (25π/4) or cos (19.6349540 . . .)
What is the Value of Cos 1125 Degrees?
The value of cos 1125 degrees in decimal is 0.707106781. . .. Cos 1125 degrees can also be expressed using the equivalent of the given angle (1125 degrees) in radians (19.63495 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1125 degrees = 1125° × (π/180°) rad = 25π/4 or 19.6349 . . .
∴ cos 1125° = cos(19.6349) = 1/√2 or 0.7071067. . .
Explanation:
For cos 1125°, the angle 1125° > 360°. Given the periodic property of the cosine function, we can represent it as cos(1125° mod 360°) = cos(45°). The angle 1125°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 1125 degrees value = 1/√2 or 0.7071067. . .
Similarly, cos 1125° can also be written as, cos 1125 degrees = (1125° + n × 360°), n ∈ Z.
⇒ cos 1125° = cos 1485° = cos 1845°, and so on.
Note: Since, cosine is an even function, the value of cos(-1125°) = cos(1125°).
Methods to Find Value of Cos 1125 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 1125° is given as 0.70710. . .. We can find the value of cos 1125 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 1125 Degrees Using Unit Circle
To find the value of cos 1125 degrees using the unit circle, represent 1125° in the form (3 × 360°) + 45° [∵ 1125°>360°] ∵ cosine is a periodic function, cos 1125° = cos 45°.
- Rotate ‘r’ anticlockwise to form 45° or 1125° angle with the positive x-axis.
- The cos of 1125 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 1125° = x = 0.7071 (approx)
Cos 1125° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 1125 degrees as:
- ± √(1-sin²(1125°))
- ± 1/√(1 + tan²(1125°))
- ± cot 1125°/√(1 + cot²(1125°))
- ±√(cosec²(1125°) - 1)/cosec 1125°
- 1/sec 1125°
Note: Since 1125° lies in the 1st Quadrant, the final value of cos 1125° will be positive.
We can use trigonometric identities to represent cos 1125° as,
- -cos(180° - 1125°) = -cos(-945°)
- -cos(180° + 1125°) = -cos 1305°
- sin(90° + 1125°) = sin 1215°
- sin(90° - 1125°) = sin(-1035°)
☛ Also Check:
FAQs on Cos 1125 Degrees
What is Cos 1125 Degrees?
Cos 1125 degrees is the value of cosine trigonometric function for an angle equal to 1125 degrees. The value of cos 1125° is 1/√2 or 0.7071 (approx)
What is the Value of Cos 1125 Degrees in Terms of Cot 1125°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 1125° can be written as cot 1125°/√(1 + cot²(1125°)). Here, the value of cot 1125° is equal to 1.
How to Find Cos 1125° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 1125° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(1125°))
- ± 1/√(1 + tan²(1125°))
- ± cot 1125°/√(1 + cot²(1125°))
- ± √(cosec²(1125°) - 1)/cosec 1125°
- 1/sec 1125°
☛ Also check: trigonometric table
What is the Value of Cos 1125° in Terms of Sec 1125°?
Since the secant function is the reciprocal of the cosine function, we can write cos 1125° as 1/sec(1125°). The value of sec 1125° is equal to 1.414213.
How to Find the Value of Cos 1125 Degrees?
The value of cos 1125 degrees can be calculated by constructing an angle of 1125° 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 1125° is equal to the x-coordinate (0.7071). ∴ cos 1125° = 0.7071.