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 y=sinxy = \sin x on the interval 0x2π0 \leq x \leq 2\pi occur where sinx=0\sin x = 0. The sine function equals zero at integer multiples of π\pi. Thus, within the given interval, the values of xx that make sinx=0\sin x = 0 are:

x=0,π, and 2πx = 0, \pi, \text{ and } 2\pi

Therefore, the correct answer is:

0,π,0, \pi, and 2π2\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=sinxy = \sin x outside the interval 0x2π0 \leq x \leq 2\pi?
  2. How would the x-intercepts change for the function y=sin(2x)y = \sin(2x)?
  3. What are the x-intercepts of the function y=cosxy = \cos x on the interval 0x2π0 \leq x \leq 2\pi?
  4. How do the x-intercepts of y=sinxy = \sin x compare with those of y=tanxy = \tan x?
  5. What is the period of the function y=sinxy = \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.

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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