Cos 765 Degrees
The value of cos 765 degrees is 0.7071067. . .. Cos 765 degrees in radians is written as cos (765° × π/180°), i.e., cos (17π/4) or cos (13.351768. . .). In this article, we will discuss the methods to find the value of cos 765 degrees with examples.
- Cos 765°: 0.7071067. . .
- Cos 765° in fraction: 1/√2
- Cos (-765 degrees): 0.7071067. . .
- Cos 765° in radians: cos (17π/4) or cos (13.3517687 . . .)
What is the Value of Cos 765 Degrees?
The value of cos 765 degrees in decimal is 0.707106781. . .. Cos 765 degrees can also be expressed using the equivalent of the given angle (765 degrees) in radians (13.35176 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 765 degrees = 765° × (π/180°) rad = 17π/4 or 13.3517 . . .
∴ cos 765° = cos(13.3517) = 1/√2 or 0.7071067. . .
Explanation:
For cos 765°, the angle 765° > 360°. Given the periodic property of the cosine function, we can represent it as cos(765° mod 360°) = cos(45°). The angle 765°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 765 degrees value = 1/√2 or 0.7071067. . .
Similarly, cos 765° can also be written as, cos 765 degrees = (765° + n × 360°), n ∈ Z.
⇒ cos 765° = cos 1125° = cos 1485°, and so on.
Note: Since, cosine is an even function, the value of cos(-765°) = cos(765°).
Methods to Find Value of Cos 765 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 765° is given as 0.70710. . .. We can find the value of cos 765 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 765 Degrees Using Unit Circle
To find the value of cos 765 degrees using the unit circle, represent 765° in the form (2 × 360°) + 45° [∵ 765°>360°] ∵ cosine is a periodic function, cos 765° = cos 45°.
- Rotate ‘r’ anticlockwise to form 45° or 765° angle with the positive x-axis.
- The cos of 765 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 765° = x = 0.7071 (approx)
Cos 765° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 765 degrees as:
- ± √(1-sin²(765°))
- ± 1/√(1 + tan²(765°))
- ± cot 765°/√(1 + cot²(765°))
- ±√(cosec²(765°) - 1)/cosec 765°
- 1/sec 765°
Note: Since 765° lies in the 1st Quadrant, the final value of cos 765° will be positive.
We can use trigonometric identities to represent cos 765° as,
- -cos(180° - 765°) = -cos(-585°)
- -cos(180° + 765°) = -cos 945°
- sin(90° + 765°) = sin 855°
- sin(90° - 765°) = sin(-675°)
☛ Also Check:
FAQs on Cos 765 Degrees
What is Cos 765 Degrees?
Cos 765 degrees is the value of cosine trigonometric function for an angle equal to 765 degrees. The value of cos 765° is 1/√2 or 0.7071 (approx)
What is the Value of Cos 765 Degrees in Terms of Tan 765°?
We know, using trig identities, we can write cos 765° as 1/√(1 + tan²(765°)). Here, the value of tan 765° is equal to 1.
How to Find the Value of Cos 765 Degrees?
The value of cos 765 degrees can be calculated by constructing an angle of 765° 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 765° is equal to the x-coordinate (0.7071). ∴ cos 765° = 0.7071.
How to Find Cos 765° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 765° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(765°))
- ± 1/√(1 + tan²(765°))
- ± cot 765°/√(1 + cot²(765°))
- ± √(cosec²(765°) - 1)/cosec 765°
- 1/sec 765°
☛ Also check: trigonometry table
What is the Value of Cos 765° in Terms of Sec 765°?
Since the secant function is the reciprocal of the cosine function, we can write cos 765° as 1/sec(765°). The value of sec 765° is equal to 1.414213.