Sin 750 Degrees
The value of sin 750 degrees is 0.5. Sin 750 degrees in radians is written as sin (750° × π/180°), i.e., sin (25π/6) or sin (13.089969. . .). In this article, we will discuss the methods to find the value of sin 750 degrees with examples.
- Sin 750°: 0.5
- Sin 750° in fraction: 1/2
- Sin (-750 degrees): -0.5
- Sin 750° in radians: sin (25π/6) or sin (13.0899693 . . .)
What is the Value of Sin 750 Degrees?
The value of sin 750 degrees in decimal is 0.5. Sin 750 degrees can also be expressed using the equivalent of the given angle (750 degrees) in radians (13.08996 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 750 degrees = 750° × (π/180°) rad = 25π/6 or 13.0899 . . .
∴ sin 750° = sin(13.0899) = 1/2 or 0.5
Explanation:
For sin 750°, the angle 750° > 360°. Given the periodic property of the sine function, we can represent it as sin(750° mod 360°) = sin(30°). The angle 750°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 750 degrees value = 1/2 or 0.5
Similarly, sin 750° can also be written as, sin 750 degrees = (750° + n × 360°), n ∈ Z.
⇒ sin 750° = sin 1110° = sin 1470°, and so on.
Note: Since, sine is an odd function, the value of sin(-750°) = -sin(750°).
Methods to Find Value of Sin 750 Degrees
The sine function is positive in the 1st quadrant. The value of sin 750° is given as 0.5. We can find the value of sin 750 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 750 Degrees Using Unit Circle
To find the value of sin 750 degrees using the unit circle, represent 750° in the form (2 × 360°) + 30° [∵ 750°>360°] ∵ sine is a periodic function, sin 750° = sin 30°.
- Rotate ‘r’ anticlockwise to form a 30° or 750° angle with the positive x-axis.
- The sin of 750 degrees equals the y-coordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of sin 750° = y = 0.5
Sin 750° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 750 degrees as:
- ± √(1-cos²(750°))
- ± tan 750°/√(1 + tan²(750°))
- ± 1/√(1 + cot²(750°))
- ± √(sec²(750°) - 1)/sec 750°
- 1/cosec 750°
Note: Since 750° lies in the 1st Quadrant, the final value of sin 750° will be positive.
We can use trigonometric identities to represent sin 750° as,
- sin(180° - 750°) = sin(-570°)
- -sin(180° + 750°) = -sin 930°
- cos(90° - 750°) = cos(-660°)
- -cos(90° + 750°) = -cos 840°
☛ Also Check:
FAQs on Sin 750 Degrees
What is Sin 750 Degrees?
Sin 750 degrees is the value of sine trigonometric function for an angle equal to 750 degrees. The value of sin 750° is 1/2 or 0.5.
How to Find the Value of Sin 750 Degrees?
The value of sin 750 degrees can be calculated by constructing an angle of 750° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sin 750° is equal to the y-coordinate (0.5). ∴ sin 750° = 0.5.
How to Find Sin 750° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 750° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(750°))
- ± tan 750°/√(1 + tan²(750°))
- ± 1/√(1 + cot²(750°))
- ± √(sec²(750°) - 1)/sec 750°
- 1/cosec 750°
☛ Also check: trigonometric table
What is the Value of Sin 750° in Terms of Sec 750°?
Since the sine function can be represented using the secant function, we can write sin 750° as √(sec²(750°) - 1)/sec 750°. The value of sec 750° is equal to 1.154701.
What is the Value of Sin 750 Degrees in Terms of Tan 750°?
We know, using trig identities, we can write sin 750° as tan 750°/√(1 + tan²(750°)). Here, the value of tan 750° is equal to 0.577350.