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:

• ± √(1-cos²(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 x-axis.
• The sin of 5pi/6 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 5pi/6 = y = 0.5

☛ Also Check:

• cos pi/3
• sin 3pi
• cos pi/2
• tan 7pi/3
• cos 11pi/6
• sin 2pi/5

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 x-axis, 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 y-coordinate (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:

• ± √(1-cos²(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.