Sin 836 Degrees
The value of sin 836 degrees is 0.8987940. . .. Sin 836 degrees in radians is written as sin (836° × π/180°), i.e., sin (209π/45) or sin (14.590952. . .). In this article, we will discuss the methods to find the value of sin 836 degrees with examples.
- Sin 836°: 0.8987940. . .
- Sin (-836 degrees): -0.8987940. . .
- Sin 836° in radians: sin (209π/45) or sin (14.5909525 . . .)
What is the Value of Sin 836 Degrees?
The value of sin 836 degrees in decimal is 0.898794046. . .. Sin 836 degrees can also be expressed using the equivalent of the given angle (836 degrees) in radians (14.59095 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 836 degrees = 836° × (π/180°) rad = 209π/45 or 14.5909 . . .
∴ sin 836° = sin(14.5909) = 0.8987940. . .
Explanation:
For sin 836°, the angle 836° > 360°. Given the periodic property of the sine function, we can represent it as sin(836° mod 360°) = sin(116°). The angle 836°, coterminal to angle 116°, is located in the Second Quadrant(Quadrant II).
Since sine function is positive in the 2nd quadrant, thus sin 836 degrees value = 0.8987940. . .
Similarly, sin 836° can also be written as, sin 836 degrees = (836° + n × 360°), n ∈ Z.
⇒ sin 836° = sin 1196° = sin 1556°, and so on.
Note: Since, sine is an odd function, the value of sin(-836°) = -sin(836°).
Methods to Find Value of Sin 836 Degrees
The sine function is positive in the 2nd quadrant. The value of sin 836° is given as 0.89879. . .. We can find the value of sin 836 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 836 Degrees Using Unit Circle
To find the value of sin 836 degrees using the unit circle, represent 836° in the form (2 × 360°) + 116° [∵ 836°>360°] ∵ sine is a periodic function, sin 836° = sin 116°.
- Rotate ‘r’ anticlockwise to form a 116° or 836° angle with the positive x-axis.
- The sin of 836 degrees equals the y-coordinate(0.8988) of the point of intersection (-0.4384, 0.8988) of unit circle and r.
Hence the value of sin 836° = y = 0.8988 (approx)
Sin 836° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 836 degrees as:
- ± √(1-cos²(836°))
- ± tan 836°/√(1 + tan²(836°))
- ± 1/√(1 + cot²(836°))
- ± √(sec²(836°) - 1)/sec 836°
- 1/cosec 836°
Note: Since 836° lies in the 2nd Quadrant, the final value of sin 836° will be positive.
We can use trigonometric identities to represent sin 836° as,
- sin(180° - 836°) = sin(-656°)
- -sin(180° + 836°) = -sin 1016°
- cos(90° - 836°) = cos(-746°)
- -cos(90° + 836°) = -cos 926°
☛ Also Check:
FAQs on Sin 836 Degrees
What is Sin 836 Degrees?
Sin 836 degrees is the value of sine trigonometric function for an angle equal to 836 degrees. The value of sin 836° is 0.8988 (approx).
How to Find the Value of Sin 836 Degrees?
The value of sin 836 degrees can be calculated by constructing an angle of 836° with the x-axis, and then finding the coordinates of the corresponding point (-0.4384, 0.8988) on the unit circle. The value of sin 836° is equal to the y-coordinate (0.8988). ∴ sin 836° = 0.8988.
How to Find Sin 836° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 836° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(836°))
- ± tan 836°/√(1 + tan²(836°))
- ± 1/√(1 + cot²(836°))
- ± √(sec²(836°) - 1)/sec 836°
- 1/cosec 836°
☛ Also check: trigonometry table
What is the Value of Sin 836° in Terms of Cosec 836°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 836° as 1/cosec(836°). The value of cosec 836° is equal to 1.11260.
What is the Value of Sin 836 Degrees in Terms of Cos 836°?
Using trigonometric identities, we can write sin 836° in terms of cos 836° as, sin(836°) = √(1-cos²(836°)). Here, the value of cos 836° is equal to -0.4383711.