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

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

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

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 \( y = \sin(x - \frac{\pi}{4}) \)?
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.

Explore how the graph of y = cos(x) is the same as y = sin(x) shifted to the left by π/2 units. Learn about phase shifts in trigonometric functions and their impact on graph transformations. Suitable for high school students studying trigonometry.

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