Sin 903 Degrees
The value of sin 903 degrees is -0.0523359. . .. Sin 903 degrees in radians is written as sin (903° × π/180°), i.e., sin (301π/60) or sin (15.760323. . .). In this article, we will discuss the methods to find the value of sin 903 degrees with examples.
- Sin 903°: -0.0523359. . .
- Sin (-903 degrees): 0.0523359. . .
- Sin 903° in radians: sin (301π/60) or sin (15.7603231 . . .)
What is the Value of Sin 903 Degrees?
The value of sin 903 degrees in decimal is -0.052335956. . .. Sin 903 degrees can also be expressed using the equivalent of the given angle (903 degrees) in radians (15.76032 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 903 degrees = 903° × (π/180°) rad = 301π/60 or 15.7603 . . .
∴ sin 903° = sin(15.7603) = -0.0523359. . .
Explanation:
For sin 903°, the angle 903° > 360°. Given the periodic property of the sine function, we can represent it as sin(903° mod 360°) = sin(183°). The angle 903°, coterminal to angle 183°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 903 degrees value = -0.0523359. . .
Similarly, sin 903° can also be written as, sin 903 degrees = (903° + n × 360°), n ∈ Z.
⇒ sin 903° = sin 1263° = sin 1623°, and so on.
Note: Since, sine is an odd function, the value of sin(-903°) = -sin(903°).
Methods to Find Value of Sin 903 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 903° is given as -0.05233. . .. We can find the value of sin 903 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 903° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 903 degrees as:
- ± √(1-cos²(903°))
- ± tan 903°/√(1 + tan²(903°))
- ± 1/√(1 + cot²(903°))
- ± √(sec²(903°) - 1)/sec 903°
- 1/cosec 903°
Note: Since 903° lies in the 3rd Quadrant, the final value of sin 903° will be negative.
We can use trigonometric identities to represent sin 903° as,
- sin(180° - 903°) = sin(-723°)
- -sin(180° + 903°) = -sin 1083°
- cos(90° - 903°) = cos(-813°)
- -cos(90° + 903°) = -cos 993°
Sin 903 Degrees Using Unit Circle
To find the value of sin 903 degrees using the unit circle, represent 903° in the form (2 × 360°) + 183° [∵ 903°>360°] ∵ sine is a periodic function, sin 903° = sin 183°.
- Rotate ‘r’ anticlockwise to form a 183° or 903° angle with the positive x-axis.
- The sin of 903 degrees equals the y-coordinate(-0.0523) of the point of intersection (-0.9986, -0.0523) of unit circle and r.
Hence the value of sin 903° = y = -0.0523 (approx)
☛ Also Check:
FAQs on Sin 903 Degrees
What is Sin 903 Degrees?
Sin 903 degrees is the value of sine trigonometric function for an angle equal to 903 degrees. The value of sin 903° is -0.0523 (approx).
How to Find Sin 903° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 903° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(903°))
- ± tan 903°/√(1 + tan²(903°))
- ± 1/√(1 + cot²(903°))
- ± √(sec²(903°) - 1)/sec 903°
- 1/cosec 903°
☛ Also check: trigonometry table
How to Find the Value of Sin 903 Degrees?
The value of sin 903 degrees can be calculated by constructing an angle of 903° with the x-axis, and then finding the coordinates of the corresponding point (-0.9986, -0.0523) on the unit circle. The value of sin 903° is equal to the y-coordinate (-0.0523). ∴ sin 903° = -0.0523.
What is the Value of Sin 903 Degrees in Terms of Cot 903°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 903° can be written as -1/√(1 + cot²(903°)). Here, the value of cot 903° is equal to 19.08113.
What is the Value of Sin 903° in Terms of Sec 903°?
Since the sine function can be represented using the secant function, we can write sin 903° as √(sec²(903°) - 1)/sec 903°. The value of sec 903° is equal to -1.001372.