Question

The angle 30 degrees is shown below in standard position, together with a unit circle. The image shows a unit circle and a right triangle in quadrant 1 with a 30-degree angle in standard position. The hypotenuse, which is also the terminal side of the angle, has a length of 1. The terminal side intersects the circle at (square root of 3 over 2, one-half). Use the coordinates of the point of intersection of the terminal side and the circle to compute sin 30

Answer 1

To calculate sin 30 degrees, use the y-coordinate of the point where the terminal side of the angle intersects the unit circle; sin 30 degrees equals 1/2.

Step-by-step explanation:

To compute sin 30 degrees, we refer to the unit circle where the angle in standard position intersects the circle at a point with coordinates (√3/2, 1/2).

According to trigonometric definitions, for a right triangle with an angle θ, the sine of the angle is the quotient of the opposite side (Ay) to the hypotenuse (A), which is represented by sin θ = Ay/A.

In the case of a 30-degree angle in a unit circle, the hypotenuse is always 1 (since it's a unit circle).

Thus, the sine of 30 degrees is simply the y-coordinate of the point where the angle's terminal side intersects the unit circle, which is 1/2.