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 is the graph of shifted to the left by units. This is because the cosine function is essentially the sine function with a phase shift of to the left. Mathematically, this can be expressed as:
Would you like more details on phase shifts and transformations of trigonometric functions?
Here are 5 questions you might consider next:
- How do you graph transformations of the sine and cosine functions?
- What is the phase shift of the function ?
- Can you explain amplitude and period changes in trigonometric functions?
- How do you find the equation of a sine function given its graph?
- 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
-
Suitable Grade Level
High School