How To Find The Value Of Sin 7𝜋/6: The Unit Circle And Reference Angle.

sin 7𝜋/6

-0.5

To find the value of sin 7𝜋/6, first we need to understand the unit circle. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane.

In order to find sin 7𝜋/6, we need to identify the reference angle. A reference angle is the acute angle between the terminal side of the angle and the x-axis.

To find the reference angle for 7𝜋/6, we need to subtract the nearest multiple of 2𝜋 from 7𝜋/6. In this case, the nearest multiple of 2𝜋 is 2𝜋, which we can subtract from 7𝜋/6 to get 7𝜋/6 – 2𝜋 = 3𝜋/6.

Since 3𝜋/6 is simplifiable to 𝜋/2 or 90 degrees, we know that the reference angle for 7𝜋/6 is 90 degrees.

Next, we need to determine the quadrant in which 7𝜋/6 lies. We know that 𝜋/6 is in the second quadrant, so 7𝜋/6 is in the fourth quadrant.

In the fourth quadrant, sine is negative. Therefore, sin 7𝜋/6 is equal to -1/2.

Therefore, sin 7𝜋/6 = -1/2.

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