Sin 5pi/12
The value of sin 5pi/12 is 0.9659258. . .. Sin 5pi/12 radians in degrees is written as sin ((5π/12) × 180°/π), i.e., sin (75°). In this article, we will discuss the methods to find the value of sin 5pi/12 with examples.
- Sin 5pi/12: (√6 + √2)/4
- Sin 5pi/12 in decimal: 0.9659258. . .
- Sin (-5pi/12): -0.9659258. . . or -(√6 + √2)/4
- Sin 5pi/12 in degrees: sin (75°)
What is the Value of Sin 5pi/12?
The value of sin 5pi/12 in decimal is 0.965925826. . .. Sin 5pi/12 can also be expressed using the equivalent of the given angle (5pi/12) in degrees (75°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/12 radians = 5pi/12 × (180°/pi) = 75° or 75 degrees
∴ sin 5pi/12 = sin 5π/12 = sin(75°) = (√6 + √2)/4 or 0.9659258. . .
Explanation:
For sin 5pi/12, the angle 5pi/12 lies between 0 and pi/2 (First Quadrant). Since sine function is positive in the first quadrant, thus sin 5pi/12 value = (√6 + √2)/4 or 0.9659258. . .
Since the sine function is a periodic function, we can represent sin 5pi/12 as, sin 5pi/12 = sin(5pi/12 + n × 2pi), n ∈ Z.
⇒ sin 5pi/12 = sin 29pi/12 = sin 53pi/12 , and so on.
Note: Since, sine is an odd function, the value of sin(-5pi/12) = -sin(5pi/12).
Methods to Find Value of Sin 5pi/12
The sine function is positive in the 1st quadrant. The value of sin 5pi/12 is given as 0.96592. . .. We can find the value of sin 5pi/12 by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 5pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 5pi/12 as:
- ± √(1-cos²(5pi/12))
- ± tan(5pi/12)/√(1 + tan²(5pi/12))
- ± 1/√(1 + cot²(5pi/12))
- ± √(sec²(5pi/12) - 1)/sec(5pi/12)
- 1/cosec(5pi/12)
Note: Since 5pi/12 lies in the 1st Quadrant, the final value of sin 5pi/12 will be positive.
We can use trigonometric identities to represent sin 5pi/12 as,
- sin(pi - 5pi/12) = sin 7pi/12
- -sin(pi + 5pi/12) = -sin 17pi/12
- cos(pi/2 - 5pi/12) = cos pi/12
- -cos(pi/2 + 5pi/12) = -cos 11pi/12
Sin 5pi/12 Using Unit Circle
To find the value of sin 5π/12 using the unit circle:
- Rotate ‘r’ anticlockwise to form 5pi/12 angle with the positive x-axis.
- The sin of 5pi/12 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 5pi/12 = y = 0.9659 (approx)
☛ Also Check:
FAQs on Sin 5pi/12
What is Sin 5pi/12?
Sin 5pi/12 is the value of sine trigonometric function for an angle equal to 5pi/12 radians. The value of sin 5pi/12 is (√6 + √2)/4 or 0.9659 (approx).
How to Find Sin 5pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 5π/12 can be given in terms of other trigonometric functions as:
- ± √(1-cos²(5pi/12))
- ± tan(5pi/12)/√(1 + tan²(5pi/12))
- ± 1/√(1 + cot²(5pi/12))
- ± √(sec²(5pi/12) - 1)/sec(5pi/12)
- 1/cosec(5pi/12)
☛ Also check: trigonometry table
How to Find the Value of Sin 5pi/12?
The value of sin 5pi/12 can be calculated by constructing an angle of 5π/12 radians 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 5pi/12 is equal to the y-coordinate (0.9659). ∴ sin 5pi/12 = 0.9659.
What is the Value of Sin 5pi/12 in Terms of Sec 5pi/12?
Since the sine function can be represented using the secant function, we can write sin 5pi/12 as √(sec²(5pi/12) - 1)/sec 5pi/12. The value of sec 5pi/12 is equal to 3.863703.
What is the Value of Sin 5pi/12 in Terms of Cot 5pi/12?
We can represent the sine function in terms of the cotangent function using trig identities, sin 5pi/12 can be written as 1/√(1 + cot²(5pi/12)). Here, the value of cot 5pi/12 is equal to 0.2679.