Sin 7pi/12
The value of sin 7pi/12 is 0.9659258. . .. Sin 7pi/12 radians in degrees is written as sin ((7π/12) × 180°/π), i.e., sin (105°). In this article, we will discuss the methods to find the value of sin 7pi/12 with examples.
 Sin 7pi/12: (√6 + √2)/4
 Sin 7pi/12 in decimal: 0.9659258. . .
 Sin (7pi/12): 0.9659258. . . or (√6 + √2)/4
 Sin 7pi/12 in degrees: sin (105°)
What is the Value of Sin 7pi/12?
The value of sin 7pi/12 in decimal is 0.965925826. . .. Sin 7pi/12 can also be expressed using the equivalent of the given angle (7pi/12) in degrees (105°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/12 radians = 7pi/12 × (180°/pi) = 105° or 105 degrees
∴ sin 7pi/12 = sin 7π/12 = sin(105°) = (√6 + √2)/4 or 0.9659258. . .
Explanation:
For sin 7pi/12, the angle 7pi/12 lies between pi/2 and pi (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 7pi/12 value = (√6 + √2)/4 or 0.9659258. . .
Since the sine function is a periodic function, we can represent sin 7pi/12 as, sin 7pi/12 = sin(7pi/12 + n × 2pi), n ∈ Z.
⇒ sin 7pi/12 = sin 31pi/12 = sin 55pi/12 , and so on.
Note: Since, sine is an odd function, the value of sin(7pi/12) = sin(7pi/12).
Methods to Find Value of Sin 7pi/12
The sine function is positive in the 2nd quadrant. The value of sin 7pi/12 is given as 0.96592. . .. We can find the value of sin 7pi/12 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 7pi/12 Using Unit Circle
To find the value of sin 7π/12 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/12 angle with the positive xaxis.
 The sin of 7pi/12 equals the ycoordinate(0.9659) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of sin 7pi/12 = y = 0.9659 (approx)
Sin 7pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 7pi/12 as:
 ± √(1cos²(7pi/12))
 ± tan(7pi/12)/√(1 + tan²(7pi/12))
 ± 1/√(1 + cot²(7pi/12))
 ± √(sec²(7pi/12)  1)/sec(7pi/12)
 1/cosec(7pi/12)
Note: Since 7pi/12 lies in the 2nd Quadrant, the final value of sin 7pi/12 will be positive.
We can use trigonometric identities to represent sin 7pi/12 as,
 sin(pi  7pi/12) = sin 5pi/12
 sin(pi + 7pi/12) = sin 19pi/12
 cos(pi/2  7pi/12) = cos(pi/12)
 cos(pi/2 + 7pi/12) = cos 13pi/12
☛ Also Check:
Examples Using Sin 7pi/12

Example 1: Find the value of sin(7pi/12) if cosec(7pi/12) is 1.0352.
Solution:
Since, sin 7pi/12 = 1/csc(7pi/12)
⇒ sin 7pi/12 = 1/1.0352 = 0.9659 
Example 2: Find the value of 5 sin(7pi/12)/7 cos(pi/12).
Solution:
Using trigonometric identities, we know, sin(7pi/12) = cos(pi/2  7pi/12) = cos(pi/12).
⇒ sin(7pi/12) = cos(pi/12)
⇒ Value of 5 sin(7pi/12)/7 cos(pi/12) = 5/7 
Example 3: Find the value of 2 × (sin(7pi/24) cos(7pi/24)). [Hint: Use sin 7pi/12 = 0.9659]
Solution:
Using the sin 2a formula,
2 sin(7pi/24) cos(7pi/24) = sin(2 × 7pi/24) = sin 7pi/12
∵ sin 7pi/12 = 0.9659
⇒ 2 × (sin(7pi/24) cos(7pi/24)) = 0.9659
FAQs on Sin 7pi/12
What is Sin 7pi/12?
Sin 7pi/12 is the value of sine trigonometric function for an angle equal to 7pi/12 radians. The value of sin 7pi/12 is (√6 + √2)/4 or 0.9659 (approx).
What is the Value of Sin 7pi/12 in Terms of Tan 7pi/12?
We know, using trig identities, we can write sin 7pi/12 as tan(7pi/12)/√(1 + tan²(7pi/12)). Here, the value of tan 7pi/12 is equal to 3.732050.
What is the Value of Sin 7pi/12 in Terms of Cosec 7pi/12?
Since the cosecant function is the reciprocal of the sine function, we can write sin 7pi/12 as 1/cosec(7pi/12). The value of cosec 7pi/12 is equal to 1.03527.
How to Find the Value of Sin 7pi/12?
The value of sin 7pi/12 can be calculated by constructing an angle of 7π/12 radians with the xaxis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of sin 7pi/12 is equal to the ycoordinate (0.9659). ∴ sin 7pi/12 = 0.9659.
How to Find Sin 7pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 7π/12 can be given in terms of other trigonometric functions as:
 ± √(1cos²(7pi/12))
 ± tan(7pi/12)/√(1 + tan²(7pi/12))
 ± 1/√(1 + cot²(7pi/12))
 ± √(sec²(7pi/12)  1)/sec(7pi/12)
 1/cosec(7pi/12)
☛ Also check: trigonometric table
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