Cot 765 Degrees

The value of cot 765 degrees is 1. Cot 765 degrees in radians is written as cot (765° × π/180°), i.e., cot (17π/4) or cot (13.351768. . .). In this article, we will discuss the methods to find the value of cot 765 degrees with examples.

• Cot 765°: 1
• Cot (-765 degrees): -1
• Cot 765° in radians: cot (17π/4) or cot (13.3517687 . . .)

What is the Value of Cot 765 Degrees?

The value of cot 765 degrees is 1. Cot 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 . . .
∴ cot 765° = cot(13.3517) = 1

Explanation:

For cot 765°, the angle 765° > 360°. We can represent cot 765° as, cot(765° mod 360°) = cot(45°). The angle 765°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since cotangent function is positive in the 1st quadrant, thus cot 765 degrees value = 1
Similarly, given the periodic property of cot 765°, it can also be written as, cot 765 degrees = (765° + n × 180°), n ∈ Z.
⇒ cot 765° = cot 945° = cot 1125°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-765°) = -cot(765°).

Methods to Find Value of Cot 765 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 765° is given as 1. We can find the value of cot 765 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 765 Degrees Using Unit Circle

To find the value of cot 765 degrees using the unit circle, represent 765° in the form (2 × 360°) + 45° [∵ 765°>360°] ∵ The angle 765° is coterminal to 45° angle and also cotangent is a periodic function, cot 765° = cot 45°.

• Rotate ‘r’ anticlockwise to form 45° or 765° angle with the positive x-axis.
• The cot of 765 degrees equals the x-coordinate(0.7071) divided by y-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.

Hence the value of cot 765° = x/y = 1

Cot 765° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 765 degrees as:

• cos(765°)/sin(765°)
• ± cos 765°/√(1 - cos²(765°))
• ± √(1 - sin²(765°))/sin 765°
• ± 1/√(sec²(765°) - 1)
• ± √(cosec²(765°) - 1)
• 1/tan 765°

Note: Since 765° lies in the 1st Quadrant, the final value of cot 765° will be positive.

We can use trigonometric identities to represent cot 765° as,

• tan (90° - 765°) = tan(-675°)
• -tan (90° + 765°) = -tan 855°
• -cot (180° - 765°) = -cot(-585°)

☛ Also Check:

• cot 180 degrees
• cot 34 degrees
• cot 765 degrees
• cot 10 degrees
• cot 11 degrees
• cot 13 degrees

FAQs on Cot 765 Degrees

What is Cot 765 Degrees?

Cot 765 degrees is the value of cotangent trigonometric function for an angle equal to 765 degrees. The value of cot 765° is 1.

How to Find the Value of Cot 765 Degrees?

The value of cot 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 cot 765° is equal to the x-coordinate(0.7071) divided by the y-coordinate (0.7071). ∴ cot 765° = 1

How to Find Cot 765° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 765° can be given in terms of other trigonometric functions as:

• cos(765°)/sin(765°)
• ± cos 765°/√(1 - cos²(765°))
• ± √(1 - sin²(765°))/sin 765°
• ± 1/√(sec²(765°) - 1)
• ± √(cosec²(765°) - 1)
• 1/tan 765°

☛ Also check: trigonometric table

What is the Value of Cot 765 Degrees in Terms of Sin 765°?

Using trigonometric identities, we can write cot 765° in terms of sin 765° as, cot(765°) = √(1 - sin²(765°))/sin 765° . Here, the value of sin 765° is equal to 0.7071.

What is the Value of Cot 765° in Terms of Cosec 765°?

Since the cotangent function can be represented using the cosecant function, we can write cot 765° as √(cosec²(765°) - 1). The value of cosec 765° is equal to 1.41421.