On the interval 0 ≤ x ≤ 2π, what are the x-intercepts of y = sinx?

0, StartFraction pi Over 2 EndFraction, and StartFraction 3 pi Over 2 EndFraction

0, π, and 2π

StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction

π and 2π only

The x-intercepts of the function \( y = \sin x \) on the interval \( 0 \leq x \leq 2\pi \) occur where \( \sin x = 0 \). The sine function equals zero at integer multiples of \( \pi \). Thus, within the given interval, the values of \( x \) that make \( \sin x = 0 \) are:

\[
x = 0, \pi, \text{ and } 2\pi
\]

Therefore, the correct answer is:

**\( 0, \pi, \) and \( 2\pi \)**

Would you like further details or explanations on this problem?

Here are 5 related questions that expand on this information:
1. What are the general x-intercepts of \( y = \sin x \) outside the interval \( 0 \leq x \leq 2\pi \)?
2. How would the x-intercepts change for the function \( y = \sin(2x) \)?
3. What are the x-intercepts of the function \( y = \cos x \) on the interval \( 0 \leq x \leq 2\pi \)?
4. How do the x-intercepts of \( y = \sin x \) compare with those of \( y = \tan x \)?
5. What is the period of the function \( y = \sin x \) and how does it relate to the location of the x-intercepts?

**Tip:** The x-intercepts of trigonometric functions often correspond to key points that can help in graphing or understanding transformations of these functions.

On the interval 0 ≤ x ≤ 2π, what are the x-intercepts of y = sinx?

Explore the x-intercepts of the function y = sin(x) on the interval 0 ≤ x ≤ 2π. This problem demonstrates key trigonometric concepts like the sine function's zeros and how to find x-intercepts. Suitable for students in Grades 9-11.

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