Sin 1500 Degrees
The value of sin 1500 degrees is 0.8660254. . .. Sin 1500 degrees in radians is written as sin (1500° × π/180°), i.e., sin (25π/3) or sin (26.179938. . .). In this article, we will discuss the methods to find the value of sin 1500 degrees with examples.
- Sin 1500°: 0.8660254. . .
- Sin 1500° in fraction: √3/2
- Sin (-1500 degrees): -0.8660254. . .
- Sin 1500° in radians: sin (25π/3) or sin (26.1799387 . . .)
What is the Value of Sin 1500 Degrees?
The value of sin 1500 degrees in decimal is 0.866025403. . .. Sin 1500 degrees can also be expressed using the equivalent of the given angle (1500 degrees) in radians (26.17993 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1500 degrees = 1500° × (π/180°) rad = 25π/3 or 26.1799 . . .
∴ sin 1500° = sin(26.1799) = √3/2 or 0.8660254. . .
Explanation:
For sin 1500°, the angle 1500° > 360°. Given the periodic property of the sine function, we can represent it as sin(1500° mod 360°) = sin(60°). The angle 1500°, coterminal to angle 60°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 1500 degrees value = √3/2 or 0.8660254. . .
Similarly, sin 1500° can also be written as, sin 1500 degrees = (1500° + n × 360°), n ∈ Z.
⇒ sin 1500° = sin 1860° = sin 2220°, and so on.
Note: Since, sine is an odd function, the value of sin(-1500°) = -sin(1500°).
Methods to Find Value of Sin 1500 Degrees
The sine function is positive in the 1st quadrant. The value of sin 1500° is given as 0.86602. . .. We can find the value of sin 1500 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 1500° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 1500 degrees as:
- ± √(1-cos²(1500°))
- ± tan 1500°/√(1 + tan²(1500°))
- ± 1/√(1 + cot²(1500°))
- ± √(sec²(1500°) - 1)/sec 1500°
- 1/cosec 1500°
Note: Since 1500° lies in the 1st Quadrant, the final value of sin 1500° will be positive.
We can use trigonometric identities to represent sin 1500° as,
- sin(180° - 1500°) = sin(-1320°)
- -sin(180° + 1500°) = -sin 1680°
- cos(90° - 1500°) = cos(-1410°)
- -cos(90° + 1500°) = -cos 1590°
Sin 1500 Degrees Using Unit Circle
To find the value of sin 1500 degrees using the unit circle, represent 1500° in the form (4 × 360°) + 60° [∵ 1500°>360°] ∵ sine is a periodic function, sin 1500° = sin 60°.
- Rotate ‘r’ anticlockwise to form a 60° or 1500° angle with the positive x-axis.
- The sin of 1500 degrees equals the y-coordinate(0.866) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of sin 1500° = y = 0.866 (approx)
☛ Also Check:
FAQs on Sin 1500 Degrees
What is Sin 1500 Degrees?
Sin 1500 degrees is the value of sine trigonometric function for an angle equal to 1500 degrees. The value of sin 1500° is √3/2 or 0.866 (approx).
What is the Value of Sin 1500 Degrees in Terms of Cot 1500°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 1500° can be written as 1/√(1 + cot²(1500°)). Here, the value of cot 1500° is equal to 0.57735.
What is the Value of Sin 1500° in Terms of Cosec 1500°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 1500° as 1/cosec(1500°). The value of cosec 1500° is equal to 1.15470.
How to Find the Value of Sin 1500 Degrees?
The value of sin 1500 degrees can be calculated by constructing an angle of 1500° with the x-axis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of sin 1500° is equal to the y-coordinate (0.866). ∴ sin 1500° = 0.866.
How to Find Sin 1500° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 1500° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(1500°))
- ± tan 1500°/√(1 + tan²(1500°))
- ± 1/√(1 + cot²(1500°))
- ± √(sec²(1500°) - 1)/sec 1500°
- 1/cosec 1500°
☛ Also check: trigonometric table