Sin 933 Degrees
The value of sin 933 degrees is -0.5446390. . .. Sin 933 degrees in radians is written as sin (933° × π/180°), i.e., sin (311π/60) or sin (16.283921. . .). In this article, we will discuss the methods to find the value of sin 933 degrees with examples.
- Sin 933°: -0.5446390. . .
- Sin (-933 degrees): 0.5446390. . .
- Sin 933° in radians: sin (311π/60) or sin (16.2839219 . . .)
What is the Value of Sin 933 Degrees?
The value of sin 933 degrees in decimal is -0.544639035. . .. Sin 933 degrees can also be expressed using the equivalent of the given angle (933 degrees) in radians (16.28392 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 933 degrees = 933° × (π/180°) rad = 311π/60 or 16.2839 . . .
∴ sin 933° = sin(16.2839) = -0.5446390. . .
Explanation:
For sin 933°, the angle 933° > 360°. Given the periodic property of the sine function, we can represent it as sin(933° mod 360°) = sin(213°). The angle 933°, coterminal to angle 213°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 933 degrees value = -0.5446390. . .
Similarly, sin 933° can also be written as, sin 933 degrees = (933° + n × 360°), n ∈ Z.
⇒ sin 933° = sin 1293° = sin 1653°, and so on.
Note: Since, sine is an odd function, the value of sin(-933°) = -sin(933°).
Methods to Find Value of Sin 933 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 933° is given as -0.54463. . .. We can find the value of sin 933 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 933° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 933 degrees as:
- ± √(1-cos²(933°))
- ± tan 933°/√(1 + tan²(933°))
- ± 1/√(1 + cot²(933°))
- ± √(sec²(933°) - 1)/sec 933°
- 1/cosec 933°
Note: Since 933° lies in the 3rd Quadrant, the final value of sin 933° will be negative.
We can use trigonometric identities to represent sin 933° as,
- sin(180° - 933°) = sin(-753°)
- -sin(180° + 933°) = -sin 1113°
- cos(90° - 933°) = cos(-843°)
- -cos(90° + 933°) = -cos 1023°
Sin 933 Degrees Using Unit Circle
To find the value of sin 933 degrees using the unit circle, represent 933° in the form (2 × 360°) + 213° [∵ 933°>360°] ∵ sine is a periodic function, sin 933° = sin 213°.
- Rotate ‘r’ anticlockwise to form a 213° or 933° angle with the positive x-axis.
- The sin of 933 degrees equals the y-coordinate(-0.5446) of the point of intersection (-0.8387, -0.5446) of unit circle and r.
Hence the value of sin 933° = y = -0.5446 (approx)
☛ Also Check:
FAQs on Sin 933 Degrees
What is Sin 933 Degrees?
Sin 933 degrees is the value of sine trigonometric function for an angle equal to 933 degrees. The value of sin 933° is -0.5446 (approx).
How to Find the Value of Sin 933 Degrees?
The value of sin 933 degrees can be calculated by constructing an angle of 933° with the x-axis, and then finding the coordinates of the corresponding point (-0.8387, -0.5446) on the unit circle. The value of sin 933° is equal to the y-coordinate (-0.5446). ∴ sin 933° = -0.5446.
What is the Value of Sin 933° in Terms of Sec 933°?
Since the sine function can be represented using the secant function, we can write sin 933° as √(sec²(933°) - 1)/sec 933°. The value of sec 933° is equal to -1.192363.
What is the Value of Sin 933 Degrees in Terms of Tan 933°?
We know, using trig identities, we can write sin 933° as -tan 933°/√(1 + tan²(933°)). Here, the value of tan 933° is equal to 0.649407.
How to Find Sin 933° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 933° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(933°))
- ± tan 933°/√(1 + tan²(933°))
- ± 1/√(1 + cot²(933°))
- ± √(sec²(933°) - 1)/sec 933°
- 1/cosec 933°
☛ Also check: trigonometry table