Cos 750 Degrees
The value of cos 750 degrees is 0.8660254. . .. Cos 750 degrees in radians is written as cos (750° × π/180°), i.e., cos (25π/6) or cos (13.089969. . .). In this article, we will discuss the methods to find the value of cos 750 degrees with examples.
- Cos 750°: 0.8660254. . .
- Cos 750° in fraction: √3/2
- Cos (-750 degrees): 0.8660254. . .
- Cos 750° in radians: cos (25π/6) or cos (13.0899693 . . .)
What is the Value of Cos 750 Degrees?
The value of cos 750 degrees in decimal is 0.866025403. . .. Cos 750 degrees can also be expressed using the equivalent of the given angle (750 degrees) in radians (13.08996 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 750 degrees = 750° × (π/180°) rad = 25π/6 or 13.0899 . . .
∴ cos 750° = cos(13.0899) = √3/2 or 0.8660254. . .
Explanation:
For cos 750°, the angle 750° > 360°. Given the periodic property of the cosine function, we can represent it as cos(750° mod 360°) = cos(30°). The angle 750°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 750 degrees value = √3/2 or 0.8660254. . .
Similarly, cos 750° can also be written as, cos 750 degrees = (750° + n × 360°), n ∈ Z.
⇒ cos 750° = cos 1110° = cos 1470°, and so on.
Note: Since, cosine is an even function, the value of cos(-750°) = cos(750°).
Methods to Find Value of Cos 750 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 750° is given as 0.86602. . .. We can find the value of cos 750 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 750 Degrees Using Unit Circle
To find the value of cos 750 degrees using the unit circle, represent 750° in the form (2 × 360°) + 30° [∵ 750°>360°] ∵ cosine is a periodic function, cos 750° = cos 30°.
- Rotate ‘r’ anticlockwise to form 30° or 750° angle with the positive x-axis.
- The cos of 750 degrees equals the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cos 750° = x = 0.866 (approx)
Cos 750° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 750 degrees as:
- ± √(1-sin²(750°))
- ± 1/√(1 + tan²(750°))
- ± cot 750°/√(1 + cot²(750°))
- ±√(cosec²(750°) - 1)/cosec 750°
- 1/sec 750°
Note: Since 750° lies in the 1st Quadrant, the final value of cos 750° will be positive.
We can use trigonometric identities to represent cos 750° as,
- -cos(180° - 750°) = -cos(-570°)
- -cos(180° + 750°) = -cos 930°
- sin(90° + 750°) = sin 840°
- sin(90° - 750°) = sin(-660°)
☛ Also Check:
FAQs on Cos 750 Degrees
What is Cos 750 Degrees?
Cos 750 degrees is the value of cosine trigonometric function for an angle equal to 750 degrees. The value of cos 750° is √3/2 or 0.866 (approx)
How to Find the Value of Cos 750 Degrees?
The value of cos 750 degrees can be calculated by constructing an angle of 750° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos 750° is equal to the x-coordinate (0.866). ∴ cos 750° = 0.866.
What is the Value of Cos 750 Degrees in Terms of Cot 750°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 750° can be written as cot 750°/√(1 + cot²(750°)). Here, the value of cot 750° is equal to 1.73205.
What is the Value of Cos 750° in Terms of Cosec 750°?
Since the cosine function can be represented using the cosecant function, we can write cos 750° as [√(cosec²(750°) - 1)/cosec 750°]. The value of cosec 750° is equal to 2.
How to Find Cos 750° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 750° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(750°))
- ± 1/√(1 + tan²(750°))
- ± cot 750°/√(1 + cot²(750°))
- ± √(cosec²(750°) - 1)/cosec 750°
- 1/sec 750°
☛ Also check: trigonometry table