Sin 7pi/6
The value of sin 7pi/6 is 0.5. Sin 7pi/6 radians in degrees is written as sin ((7π/6) × 180°/π), i.e., sin (210°). In this article, we will discuss the methods to find the value of sin 7pi/6 with examples.
 Sin 7pi/6: (1/2)
 Sin 7pi/6 in decimal: 0.5
 Sin (7pi/6): 0.5 or 1/2
 Sin 7pi/6 in degrees: sin (210°)
What is the Value of Sin 7pi/6?
The value of sin 7pi/6 in decimal is 0.5. Sin 7pi/6 can also be expressed using the equivalent of the given angle (7pi/6) in degrees (210°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/6 radians = 7pi/6 × (180°/pi) = 210° or 210 degrees
∴ sin 7pi/6 = sin 7π/6 = sin(210°) = (1/2) or 0.5
Explanation:
For sin 7pi/6, the angle 7pi/6 lies between pi and 3pi/2 (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 7pi/6 value = (1/2) or 0.5
Since the sine function is a periodic function, we can represent sin 7pi/6 as, sin 7pi/6 = sin(7pi/6 + n × 2pi), n ∈ Z.
⇒ sin 7pi/6 = sin 19pi/6 = sin 31pi/6 , and so on.
Note: Since, sine is an odd function, the value of sin(7pi/6) = sin(7pi/6).
Methods to Find Value of Sin 7pi/6
The sine function is negative in the 3rd quadrant. The value of sin 7pi/6 is given as 0.5. We can find the value of sin 7pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 7pi/6 Using Unit Circle
To find the value of sin 7π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/6 angle with the positive xaxis.
 The sin of 7pi/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 7pi/6 = y = 0.5
Sin 7pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 7pi/6 as:
 ± √(1cos²(7pi/6))
 ± tan(7pi/6)/√(1 + tan²(7pi/6))
 ± 1/√(1 + cot²(7pi/6))
 ± √(sec²(7pi/6)  1)/sec(7pi/6)
 1/cosec(7pi/6)
Note: Since 7pi/6 lies in the 3rd Quadrant, the final value of sin 7pi/6 will be negative.
We can use trigonometric identities to represent sin 7pi/6 as,
 sin(pi  7pi/6) = sin(pi/6)
 sin(pi + 7pi/6) = sin 13pi/6
 cos(pi/2  7pi/6) = cos(2pi/3)
 cos(pi/2 + 7pi/6) = cos 5pi/3
☛ Also Check:
Examples Using Sin 7pi/6

Example 1: Find the value of 5 sin(7pi/6)/7 cos(2pi/3).
Solution:
Using trigonometric identities, we know, sin(7pi/6) = cos(pi/2  7pi/6) = cos(2pi/3).
⇒ sin(7pi/6) = cos(2pi/3)
⇒ Value of 5 sin(7pi/6)/7 cos(2pi/3) = 5/7 
Example 2: Find the value of sin(7pi/6) if cosec(7pi/6) is 2.
Solution:
Since, sin 7pi/6 = 1/csc(7pi/6)
⇒ sin 7pi/6 = 1/(2) = 0.5 
Example 3: Simplify: 7 (sin(7pi/6)/sin(19pi/6))
Solution:
We know sin 7pi/6 = sin 19pi/6
⇒ 7 sin(7pi/6)/sin(19pi/6) = 7(sin(7pi/6)/sin(7pi/6))
= 7(1) = 7
FAQs on Sin 7pi/6
What is Sin 7pi/6?
Sin 7pi/6 is the value of sine trigonometric function for an angle equal to 7pi/6 radians. The value of sin 7pi/6 is (1/2) or 0.5.
How to Find the Value of Sin 7pi/6?
The value of sin 7pi/6 can be calculated by constructing an angle of 7π/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 7pi/6 is equal to the ycoordinate (0.5). ∴ sin 7pi/6 = 0.5.
How to Find Sin 7pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 7π/6 can be given in terms of other trigonometric functions as:
 ± √(1cos²(7pi/6))
 ± tan(7pi/6)/√(1 + tan²(7pi/6))
 ± 1/√(1 + cot²(7pi/6))
 ± √(sec²(7pi/6)  1)/sec(7pi/6)
 1/cosec(7pi/6)
☛ Also check: trigonometry table
What is the Value of Sin 7pi/6 in Terms of Cosec 7pi/6?
Since the cosecant function is the reciprocal of the sine function, we can write sin 7pi/6 as 1/cosec(7pi/6). The value of cosec 7pi/6 is equal to 2.
What is the Value of Sin 7pi/6 in Terms of Tan 7pi/6?
We know, using trig identities, we can write sin 7pi/6 as tan(7pi/6)/√(1 + tan²(7pi/6)). Here, the value of tan 7pi/6 is equal to 0.577350.
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