Math Problem Statement
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
Solution
The x-intercepts of the function on the interval occur where . The sine function equals zero at integer multiples of . Thus, within the given interval, the values of that make are:
Therefore, the correct answer is:
and
Would you like further details or explanations on this problem?
Here are 5 related questions that expand on this information:
- What are the general x-intercepts of outside the interval ?
- How would the x-intercepts change for the function ?
- What are the x-intercepts of the function on the interval ?
- How do the x-intercepts of compare with those of ?
- What is the period of the function 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.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Sine Function
X-Intercepts
Formulas
sin(x) = 0
Theorems
Sine Function X-Intercepts Theorem
Suitable Grade Level
Grades 9-11