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The problem asks to complete the values for the sine of common angles using the given options. The sine values for the angles \(30^\circ\), \(45^\circ\), and \(60^\circ\) are standard trigonometric values. Let's assign the correct options for each:

1. \( \sin 30^\circ = \frac{1}{2} \)
2. \( \sin 45^\circ = \frac{1}{\sqrt{2}} \) (or equivalently \( \frac{\sqrt{2}}{2} \))
3. \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)

Now, we match these values with the options given:

- \( \sin 30^\circ = \frac{1}{2} \) (Option with \( \frac{1}{2} \))
- \( \sin 45^\circ = \frac{1}{\sqrt{2}} \) (Option with \( \frac{1}{\sqrt{2}} \))
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \) (Option with \( \frac{\sqrt{3}}{2} \))

Would you like further details or have any other questions? Here are five related questions for further practice:

1. What is \( \cos 30^\circ \)?
2. What is \( \tan 45^\circ \)?
3. What is \( \sin 90^\circ \)?
4. How do you derive the sine values for \(30^\circ\), \(45^\circ\), and \(60^\circ\) geometrically?
5. What are the exact trigonometric values for cosine of the same angles?

**Tip:** Remember that the sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse.

Copy and complete each of the equalities below using the options given: a) sin 30°, b) sin 45°, c) sin 60°.

Solve for the sine values of 30°, 45°, and 60° by selecting the correct values from the options provided. This problem covers key trigonometric concepts suitable for students in Grades 9-12.

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