Tan 765 Degrees
The value of tan 765 degrees is 1. Tan 765 degrees in radians is written as tan (765° × π/180°), i.e., tan (17π/4) or tan (13.351768. . .). In this article, we will discuss the methods to find the value of tan 765 degrees with examples.
- Tan 765°: 1
- Tan (-765 degrees): -1
- Tan 765° in radians: tan (17π/4) or tan (13.3517687 . . .)
What is the Value of Tan 765 Degrees?
The value of tan 765 degrees is 1. Tan 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 . . .
∴ tan 765° = tan(13.3517) = 1
Explanation:
For tan 765°, the angle 765° > 360°. We can represent tan 765° as, tan(765° mod 360°) = tan(45°). The angle 765°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since tangent function is positive in the 1st quadrant, thus tan 765 degrees value = 1
Similarly, given the periodic property of tan 765°, it can also be written as, tan 765 degrees = (765° + n × 180°), n ∈ Z.
⇒ tan 765° = tan 945° = tan 1125°, and so on.
Note: Since, tangent is an odd function, the value of tan(-765°) = -tan(765°).
Methods to Find Value of Tan 765 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 765° is given as 1. We can find the value of tan 765 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 765 Degrees Using Unit Circle
To find the value of tan 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 tangent is a periodic function, tan 765° = tan 45°.
- Rotate ‘r’ anticlockwise to form 45° or 765° angle with the positive x-axis.
- The tan of 765 degrees equals the y-coordinate(0.7071) divided by x-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of tan 765° = y/x = 1
Tan 765° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 765 degrees as:
- sin(765°)/cos(765°)
- ± sin 765°/√(1 - sin²(765°))
- ± √(1 - cos²(765°))/cos 765°
- ± 1/√(cosec²(765°) - 1)
- ± √(sec²(765°) - 1)
- 1/cot 765°
Note: Since 765° lies in the 1st Quadrant, the final value of tan 765° will be positive.
We can use trigonometric identities to represent tan 765° as,
- cot(90° - 765°) = cot(-675°)
- -cot(90° + 765°) = -cot 855°
- -tan (180° - 765°) = -tan(-585°)
☛ Also Check:
FAQs on Tan 765 Degrees
What is Tan 765 Degrees?
Tan 765 degrees is the value of tangent trigonometric function for an angle equal to 765 degrees. The value of tan 765° is 1.
How to Find Tan 765° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 765° can be given in terms of other trigonometric functions as:
- sin(765°)/cos(765°)
- ± sin 765°/√(1 - sin²(765°))
- ± √(1 - cos²(765°))/cos 765°
- ± 1/√(cosec²(765°) - 1)
- ± √(sec²(765°) - 1)
- 1/cot 765°
☛ Also check: trigonometric table
What is the Value of Tan 765 Degrees in Terms of Cos 765°?
We know, using trig identities, we can write tan 765° as √(1 - cos²(765°))/cos 765°. Here, the value of cos 765° is equal to 0.707106.
How to Find the Value of Tan 765 Degrees?
The value of tan 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 tan 765° is equal to the y-coordinate(0.7071) divided by the x-coordinate (0.7071). ∴ tan 765° = 1
What is the Exact Value of tan 765 Degrees?
The exact value of tan 765 degrees is 1.