Sin 656 Degrees
The value of sin 656 degrees is -0.8987940. . .. Sin 656 degrees in radians is written as sin (656° × π/180°), i.e., sin (164π/45) or sin (11.449359. . .). In this article, we will discuss the methods to find the value of sin 656 degrees with examples.
- Sin 656°: -0.8987940. . .
- Sin (-656 degrees): 0.8987940. . .
- Sin 656° in radians: sin (164π/45) or sin (11.4493598 . . .)
What is the Value of Sin 656 Degrees?
The value of sin 656 degrees in decimal is -0.898794046. . .. Sin 656 degrees can also be expressed using the equivalent of the given angle (656 degrees) in radians (11.44935 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 656 degrees = 656° × (π/180°) rad = 164π/45 or 11.4493 . . .
∴ sin 656° = sin(11.4493) = -0.8987940. . .
Explanation:
For sin 656°, the angle 656° > 360°. Given the periodic property of the sine function, we can represent it as sin(656° mod 360°) = sin(296°). The angle 656°, coterminal to angle 296°, is located in the Fourth Quadrant(Quadrant IV).
Since sine function is negative in the 4th quadrant, thus sin 656 degrees value = -0.8987940. . .
Similarly, sin 656° can also be written as, sin 656 degrees = (656° + n × 360°), n ∈ Z.
⇒ sin 656° = sin 1016° = sin 1376°, and so on.
Note: Since, sine is an odd function, the value of sin(-656°) = -sin(656°).
Methods to Find Value of Sin 656 Degrees
The sine function is negative in the 4th quadrant. The value of sin 656° is given as -0.89879. . .. We can find the value of sin 656 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 656 Degrees Using Unit Circle
To find the value of sin 656 degrees using the unit circle, represent 656° in the form (1 × 360°) + 296° [∵ 656°>360°] ∵ sine is a periodic function, sin 656° = sin 296°.
- Rotate ‘r’ anticlockwise to form a 296° or 656° angle with the positive x-axis.
- The sin of 656 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 656° = y = -0.8988 (approx)
Sin 656° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 656 degrees as:
- ± √(1-cos²(656°))
- ± tan 656°/√(1 + tan²(656°))
- ± 1/√(1 + cot²(656°))
- ± √(sec²(656°) - 1)/sec 656°
- 1/cosec 656°
Note: Since 656° lies in the 4th Quadrant, the final value of sin 656° will be negative.
We can use trigonometric identities to represent sin 656° as,
- sin(180° - 656°) = sin(-476°)
- -sin(180° + 656°) = -sin 836°
- cos(90° - 656°) = cos(-566°)
- -cos(90° + 656°) = -cos 746°
☛ Also Check:
FAQs on Sin 656 Degrees
What is Sin 656 Degrees?
Sin 656 degrees is the value of sine trigonometric function for an angle equal to 656 degrees. The value of sin 656° is -0.8988 (approx).
What is the Value of Sin 656 Degrees in Terms of Cos 656°?
Using trigonometric identities, we can write sin 656° in terms of cos 656° as, sin(656°) = -√(1-cos²(656°)). Here, the value of cos 656° is equal to 0.4383711.
How to Find the Value of Sin 656 Degrees?
The value of sin 656 degrees can be calculated by constructing an angle of 656° 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 656° is equal to the y-coordinate (-0.8988). ∴ sin 656° = -0.8988.
What is the Value of Sin 656° in Terms of Sec 656°?
Since the sine function can be represented using the secant function, we can write sin 656° as -√(sec²(656°) - 1)/sec 656°. The value of sec 656° is equal to 2.281172.
How to Find Sin 656° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 656° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(656°))
- ± tan 656°/√(1 + tan²(656°))
- ± 1/√(1 + cot²(656°))
- ± √(sec²(656°) - 1)/sec 656°
- 1/cosec 656°
☛ Also check: trigonometry table