Sin 75 Degrees
The value of sin 75 degrees is 0.9659258. . .. Sin 75 degrees in radians is written as sin (75° × π/180°), i.e., sin (5π/12) or sin (1.308996. . .). In this article, we will discuss the methods to find the value of sin 75 degrees with examples.
- Sin 75°: 0.9659258. . .
- Sin 75° in fraction: (√6 + √2)/4
- Sin (-75 degrees): -0.9659258. . .
- Sin 75° in radians: sin (5π/12) or sin (1.3089969 . . .)
What is the Value of Sin 75 Degrees?
The value of sin 75 degrees in decimal is 0.965925826. . .. Sin 75 degrees can also be expressed using the equivalent of the given angle (75 degrees) in radians (1.30899 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 75 degrees = 75° × (π/180°) rad = 5π/12 or 1.3089 . . .
∴ sin 75° = sin(1.3089) = (√6 + √2)/4 or 0.9659258. . .
Explanation:
For sin 75 degrees, the angle 75° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 75° value = (√6 + √2)/4 or 0.9659258. . .
Since the sine function is a periodic function, we can represent sin 75° as, sin 75 degrees = sin(75° + n × 360°), n ∈ Z.
⇒ sin 75° = sin 435° = sin 795°, and so on.
Note: Since, sine is an odd function, the value of sin(-75°) = -sin(75°).
Methods to Find Value of Sin 75 Degrees
The sine function is positive in the 1st quadrant. The value of sin 75° is given as 0.96592. . .. We can find the value of sin 75 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 75° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 75 degrees as:
- ± √(1-cos²(75°))
- ± tan 75°/√(1 + tan²(75°))
- ± 1/√(1 + cot²(75°))
- ± √(sec²(75°) - 1)/sec 75°
- 1/cosec 75°
Note: Since 75° lies in the 1st Quadrant, the final value of sin 75° will be positive.
We can use trigonometric identities to represent sin 75° as,
- sin(180° - 75°) = sin 105°
- -sin(180° + 75°) = -sin 255°
- cos(90° - 75°) = cos 15°
- -cos(90° + 75°) = -cos 165°
Sin 75 Degrees Using Unit Circle
To find the value of sin 75 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 75° angle with the positive x-axis.
- The sin of 75 degrees equals the y-coordinate(0.9659) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of sin 75° = y = 0.9659 (approx)
☛ Also Check:
FAQs on Sin 75 Degrees
What is Sin 75 Degrees?
Sin 75 degrees is the value of sine trigonometric function for an angle equal to 75 degrees. The value of sin 75° is (√6 + √2)/4 or 0.9659 (approx).
How to Find the Value of Sin 75 Degrees?
The value of sin 75 degrees can be calculated by constructing an angle of 75° with the x-axis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of sin 75° is equal to the y-coordinate (0.9659). ∴ sin 75° = 0.9659.
What is the Value of Sin 75 Degrees in Terms of Tan 75°?
We know, using trig identities, we can write sin 75° as tan 75°/√(1 + tan²(75°)). Here, the value of tan 75° is equal to 3.732050.
What is the Value of Sin 75° in Terms of Sec 75°?
Since the sine function can be represented using the secant function, we can write sin 75° as √(sec²(75°) - 1)/sec 75°. The value of sec 75° is equal to 3.863703.
How to Find Sin 75° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 75° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(75°))
- ± tan 75°/√(1 + tan²(75°))
- ± 1/√(1 + cot²(75°))
- ± √(sec²(75°) - 1)/sec 75°
- 1/cosec 75°
☛ Also check: trigonometric table