Math Problem Statement

the graph of y=cosx is the graph of which function shifted, or translated, to the left units?

Solution

The graph of y=cosxy = \cos x is the graph of y=sinxy = \sin x shifted to the left by π2\frac{\pi}{2} units. This is because the cosine function is essentially the sine function with a phase shift of π2\frac{\pi}{2} to the left. Mathematically, this can be expressed as:

cosx=sin(x+π2)\cos x = \sin \left( x + \frac{\pi}{2} \right)

Would you like more details on phase shifts and transformations of trigonometric functions?

Here are 5 questions you might consider next:

  1. How do you graph transformations of the sine and cosine functions?
  2. What is the phase shift of the function y=sin(xπ4)y = \sin(x - \frac{\pi}{4})?
  3. Can you explain amplitude and period changes in trigonometric functions?
  4. How do you find the equation of a sine function given its graph?
  5. What are the key differences between sine and cosine functions?

Tip: When working with trigonometric functions, always pay attention to phase shifts, which are horizontal translations, and how they affect the graph of the function.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Trigonometric Functions
Phase Shifts

Formulas

y = \cos x = \sin \left( x + \frac{\pi}{2} \right)

Theorems

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Suitable Grade Level

High School