Find the Exact Value sin(30)

Problem

sin(30)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle. The angle 30 is one of the standard angles used in trigonometry.

2. Recall the properties of a 30−60−90 triangle. In such a triangle, the side opposite the 30 angle is half the length of the hypotenuse.

3. Apply the definition of the sine function, which is the ratio of the length of the opposite side to the length of the hypotenuse.

4. Calculate the ratio using a hypotenuse of 1 and an opposite side of 1/2

sin(30)=opposite/hypotenuse

sin(30)=(1/2)/1

Final Answer

sin(30)=1/2

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