Sin 5pi/6
The value of sin 5pi/6 is 0.5. Sin 5pi/6 radians in degrees is written as sin ((5π/6) × 180°/π), i.e., sin (150°). In this article, we will discuss the methods to find the value of sin 5pi/6 with examples.
 Sin 5pi/6: 1/2
 Sin 5pi/6 in decimal: 0.5
 Sin (5pi/6): 0.5 or (1/2)
 Sin 5pi/6 in degrees: sin (150°)
What is the Value of Sin 5pi/6?
The value of sin 5pi/6 in decimal is 0.5. Sin 5pi/6 can also be expressed using the equivalent of the given angle (5pi/6) in degrees (150°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/6 radians = 5pi/6 × (180°/pi) = 150° or 150 degrees
∴ sin 5pi/6 = sin 5π/6 = sin(150°) = 1/2 or 0.5
Explanation:
For sin 5pi/6, the angle 5pi/6 lies between pi/2 and pi (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 5pi/6 value = 1/2 or 0.5
Since the sine function is a periodic function, we can represent sin 5pi/6 as, sin 5pi/6 = sin(5pi/6 + n × 2pi), n ∈ Z.
⇒ sin 5pi/6 = sin 17pi/6 = sin 29pi/6 , and so on.
Note: Since, sine is an odd function, the value of sin(5pi/6) = sin(5pi/6).
Methods to Find Value of Sin 5pi/6
The sine function is positive in the 2nd quadrant. The value of sin 5pi/6 is given as 0.5. We can find the value of sin 5pi/6 by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 5pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 5pi/6 as:
 ± √(1cos²(5pi/6))
 ± tan(5pi/6)/√(1 + tan²(5pi/6))
 ± 1/√(1 + cot²(5pi/6))
 ± √(sec²(5pi/6)  1)/sec(5pi/6)
 1/cosec(5pi/6)
Note: Since 5pi/6 lies in the 2nd Quadrant, the final value of sin 5pi/6 will be positive.
We can use trigonometric identities to represent sin 5pi/6 as,
 sin(pi  5pi/6) = sin pi/6
 sin(pi + 5pi/6) = sin 11pi/6
 cos(pi/2  5pi/6) = cos(pi/3)
 cos(pi/2 + 5pi/6) = cos 4pi/3
Sin 5pi/6 Using Unit Circle
To find the value of sin 5π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/6 angle with the positive xaxis.
 The sin of 5pi/6 equals the ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of sin 5pi/6 = y = 0.5
☛ Also Check:
Examples Using Sin 5pi/6

Example 1: Simplify: 3 (sin(5pi/6)/sin(17pi/6))
Solution:
We know sin 5pi/6 = sin 17pi/6
⇒ 3 sin(5pi/6)/sin(17pi/6) = 3(sin(5pi/6)/sin(5pi/6))
= 3(1) = 3 
Example 2: Using the value of sin 5pi/6, solve: (1cos²(5pi/6)).
Solution:
We know, (1cos²(5pi/6)) = (sin²(5pi/6)) = 0.25
⇒ (1cos²(5pi/6)) = 0.25 
Example 3: Find the value of 5 sin(5pi/6)/7 cos(pi/3).
Solution:
Using trigonometric identities, we know, sin(5pi/6) = cos(pi/2  5pi/6) = cos(pi/3).
⇒ sin(5pi/6) = cos(pi/3)
⇒ Value of 5 sin(5pi/6)/7 cos(pi/3) = 5/7
FAQs on Sin 5pi/6
What is Sin 5pi/6?
Sin 5pi/6 is the value of sine trigonometric function for an angle equal to 5pi/6 radians. The value of sin 5pi/6 is 1/2 or 0.5.
What is the Value of Sin 5pi/6 in Terms of Sec 5pi/6?
Since the sine function can be represented using the secant function, we can write sin 5pi/6 as √(sec²(5pi/6)  1)/sec 5pi/6. The value of sec 5pi/6 is equal to 1.154700.
How to Find the Value of Sin 5pi/6?
The value of sin 5pi/6 can be calculated by constructing an angle of 5π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sin 5pi/6 is equal to the ycoordinate (0.5). ∴ sin 5pi/6 = 0.5.
How to Find Sin 5pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 5π/6 can be given in terms of other trigonometric functions as:
 ± √(1cos²(5pi/6))
 ± tan(5pi/6)/√(1 + tan²(5pi/6))
 ± 1/√(1 + cot²(5pi/6))
 ± √(sec²(5pi/6)  1)/sec(5pi/6)
 1/cosec(5pi/6)
☛ Also check: trigonometric table
What is the Value of Sin 5pi/6 in Terms of Tan 5pi/6?
We know, using trig identities, we can write sin 5pi/6 as tan(5pi/6)/√(1 + tan²(5pi/6)). Here, the value of tan 5pi/6 is equal to 0.577350.
visual curriculum