Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
sin(𝜃) = 
1
2


To solve the equation \( \sin(\theta) = \frac{1}{2} \), we find the angles where the sine function equals \( \frac{1}{2} \).

The general solutions for \( \theta \) are:

1. \( \theta = \frac{\pi}{6} + 2k\pi \) (first quadrant)
2. \( \theta = \frac{5\pi}{6} + 2k\pi \) (second quadrant)

Where \( k \) is any integer.

In degrees, these solutions are:

1. \( \theta = 30^\circ + 360k \)
2. \( \theta = 150^\circ + 360k \)

Thus, the solutions are:

- In radians: \( \frac{\pi}{6} + 2k\pi, \frac{5\pi}{6} + 2k\pi \)
- In degrees: \( 30^\circ + 360k, 150^\circ + 360k \)

If rounded to two decimal places, the values are:

- Radians: \( 0.52 + 6.28k, 2.62 + 6.28k \)
- Degrees: \( 30 + 360k, 150 + 360k \)

Would you like further details or explanations? Here are some related questions:

1. What is the sine function, and how does it behave in different quadrants?
2. Can you explain how to find the general solutions for other trigonometric equations?
3. How do you convert between radians and degrees?
4. What are the implications of periodicity in trigonometric functions?
5. Can you provide examples of solving other trigonometric equations? 

**Tip:** Always remember that the sine function is periodic, so you can add or subtract multiples of \( 2\pi \) (or \( 360^\circ \)) to find additional solutions.

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) sin(𝜃) = 1/2

Explore how to solve the equation sin(𝜃) = 1/2, resulting in general solutions in radians and degrees. This guide includes rounded values and covers key concepts in trigonometry, suitable for students in Grades 10-12.

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