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 x-axis.
• The sin of 7pi/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 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:

• ± √(1-cos²(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:

• tan 11pi 6
• cos 10pi/3
• cos 5pi/12
• sin 7pi/4
• tan pi/8
• cos 2pi/8

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 x-axis, 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 y-coordinate (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:

• ± √(1-cos²(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