Sin 765 Degrees
The value of sin 765 degrees is 0.7071067. . .. Sin 765 degrees in radians is written as sin (765° × π/180°), i.e., sin (17π/4) or sin (13.351768. . .). In this article, we will discuss the methods to find the value of sin 765 degrees with examples.
- Sin 765°: 0.7071067. . .
- Sin 765° in fraction: 1/√2
- Sin (-765 degrees): -0.7071067. . .
- Sin 765° in radians: sin (17π/4) or sin (13.3517687 . . .)
What is the Value of Sin 765 Degrees?
The value of sin 765 degrees in decimal is 0.707106781. . .. Sin 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 . . .
∴ sin 765° = sin(13.3517) = 1/√2 or 0.7071067. . .
Explanation:
For sin 765°, the angle 765° > 360°. Given the periodic property of the sine function, we can represent it as sin(765° mod 360°) = sin(45°). The angle 765°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 765 degrees value = 1/√2 or 0.7071067. . .
Similarly, sin 765° can also be written as, sin 765 degrees = (765° + n × 360°), n ∈ Z.
⇒ sin 765° = sin 1125° = sin 1485°, and so on.
Note: Since, sine is an odd function, the value of sin(-765°) = -sin(765°).
Methods to Find Value of Sin 765 Degrees
The sine function is positive in the 1st quadrant. The value of sin 765° is given as 0.70710. . .. We can find the value of sin 765 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 765 Degrees Using Unit Circle
To find the value of sin 765 degrees using the unit circle, represent 765° in the form (2 × 360°) + 45° [∵ 765°>360°] ∵ sine is a periodic function, sin 765° = sin 45°.
- Rotate ‘r’ anticlockwise to form a 45° or 765° angle with the positive x-axis.
- The sin of 765 degrees equals the y-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of sin 765° = y = 0.7071 (approx)
Sin 765° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 765 degrees as:
- ± √(1-cos²(765°))
- ± tan 765°/√(1 + tan²(765°))
- ± 1/√(1 + cot²(765°))
- ± √(sec²(765°) - 1)/sec 765°
- 1/cosec 765°
Note: Since 765° lies in the 1st Quadrant, the final value of sin 765° will be positive.
We can use trigonometric identities to represent sin 765° as,
- sin(180° - 765°) = sin(-585°)
- -sin(180° + 765°) = -sin 945°
- cos(90° - 765°) = cos(-675°)
- -cos(90° + 765°) = -cos 855°
☛ Also Check:
FAQs on Sin 765 Degrees
What is Sin 765 Degrees?
Sin 765 degrees is the value of sine trigonometric function for an angle equal to 765 degrees. The value of sin 765° is 1/√2 or 0.7071 (approx).
What is the Exact Value of sin 765 Degrees?
The exact value of sin 765 degrees can be given accurately up to 8 decimal places as 0.70710678 and 1/√2 in fraction.
How to Find the Value of Sin 765 Degrees?
The value of sin 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 sin 765° is equal to the y-coordinate (0.7071). ∴ sin 765° = 0.7071.
How to Find Sin 765° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 765° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(765°))
- ± tan 765°/√(1 + tan²(765°))
- ± 1/√(1 + cot²(765°))
- ± √(sec²(765°) - 1)/sec 765°
- 1/cosec 765°
☛ Also check: trigonometric table
What is the Value of Sin 765 Degrees in Terms of Cot 765°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 765° can be written as 1/√(1 + cot²(765°)). Here, the value of cot 765° is equal to 1.