Sin 756 Degrees
The value of sin 756 degrees is 0.5877852. . .. Sin 756 degrees in radians is written as sin (756° × π/180°), i.e., sin (21π/5) or sin (13.194689. . .). In this article, we will discuss the methods to find the value of sin 756 degrees with examples.
- Sin 756°: 0.5877852. . .
- Sin 756° in fraction: √(10 - 2√5)/4
- Sin (-756 degrees): -0.5877852. . .
- Sin 756° in radians: sin (21π/5) or sin (13.1946891 . . .)
What is the Value of Sin 756 Degrees?
The value of sin 756 degrees in decimal is 0.587785252. . .. Sin 756 degrees can also be expressed using the equivalent of the given angle (756 degrees) in radians (13.19468 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 756 degrees = 756° × (π/180°) rad = 21π/5 or 13.1946 . . .
∴ sin 756° = sin(13.1946) = √(10 - 2√5)/4 or 0.5877852. . .
Explanation:
For sin 756°, the angle 756° > 360°. Given the periodic property of the sine function, we can represent it as sin(756° mod 360°) = sin(36°). The angle 756°, coterminal to angle 36°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 756 degrees value = √(10 - 2√5)/4 or 0.5877852. . .
Similarly, sin 756° can also be written as, sin 756 degrees = (756° + n × 360°), n ∈ Z.
⇒ sin 756° = sin 1116° = sin 1476°, and so on.
Note: Since, sine is an odd function, the value of sin(-756°) = -sin(756°).
Methods to Find Value of Sin 756 Degrees
The sine function is positive in the 1st quadrant. The value of sin 756° is given as 0.58778. . .. We can find the value of sin 756 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 756° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 756 degrees as:
- ± √(1-cos²(756°))
- ± tan 756°/√(1 + tan²(756°))
- ± 1/√(1 + cot²(756°))
- ± √(sec²(756°) - 1)/sec 756°
- 1/cosec 756°
Note: Since 756° lies in the 1st Quadrant, the final value of sin 756° will be positive.
We can use trigonometric identities to represent sin 756° as,
- sin(180° - 756°) = sin(-576°)
- -sin(180° + 756°) = -sin 936°
- cos(90° - 756°) = cos(-666°)
- -cos(90° + 756°) = -cos 846°
Sin 756 Degrees Using Unit Circle
To find the value of sin 756 degrees using the unit circle, represent 756° in the form (2 × 360°) + 36° [∵ 756°>360°] ∵ sine is a periodic function, sin 756° = sin 36°.
- Rotate ‘r’ anticlockwise to form a 36° or 756° angle with the positive x-axis.
- The sin of 756 degrees equals the y-coordinate(0.5878) of the point of intersection (0.809, 0.5878) of unit circle and r.
Hence the value of sin 756° = y = 0.5878 (approx)
☛ Also Check:
FAQs on Sin 756 Degrees
What is Sin 756 Degrees?
Sin 756 degrees is the value of sine trigonometric function for an angle equal to 756 degrees. The value of sin 756° is √(10 - 2√5)/4 or 0.5878 (approx).
What is the Value of Sin 756 Degrees in Terms of Cos 756°?
Using trigonometric identities, we can write sin 756° in terms of cos 756° as, sin(756°) = √(1-cos²(756°)). Here, the value of cos 756° is equal to 0.8090169.
What is the Exact Value of sin 756 Degrees?
The exact value of sin 756 degrees can be given accurately up to 8 decimal places as 0.58778525 and √(10 - 2√5)/4 in fraction.
How to Find Sin 756° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 756° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(756°))
- ± tan 756°/√(1 + tan²(756°))
- ± 1/√(1 + cot²(756°))
- ± √(sec²(756°) - 1)/sec 756°
- 1/cosec 756°
☛ Also check: trigonometry table
How to Find the Value of Sin 756 Degrees?
The value of sin 756 degrees can be calculated by constructing an angle of 756° with the x-axis, and then finding the coordinates of the corresponding point (0.809, 0.5878) on the unit circle. The value of sin 756° is equal to the y-coordinate (0.5878). ∴ sin 756° = 0.5878.