How to Evaluate sin 30 degrees on the Unit Circle

Step-by-step solution

1. Find 30 degrees on the unit circle.

   $$30^\circ = \frac{\pi}{6}$$

   Why: The unit circle labels angles in both degrees and radians.

2. Read the y-coordinate of the point.

   $$\sin\theta = y$$

   Why: The sine of an angle is the y-coordinate on the unit circle.

3. Write the exact value.

   $$\sin 30^\circ = \frac{1}{2}$$

   Why: The point at 30 degrees is halfway up, so y is one half.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\sin 0^\circ$

   Show answer

   $0$

2. 2

   $\sin 90^\circ$

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   $1$

3. 3

   $\cos 0^\circ$

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   $1$

4. 4

   $\cos 60^\circ$

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   $\frac{1}{2}$

5. 5

   $\tan 45^\circ$

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   $1$