## vera_ewing one year ago What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2?

1. Michele_Laino

hint: the amplitude of your function is 2, since we have: $- 2 \leqslant 2\cos \left( {\pi x} \right) \leqslant 2$

2. Michele_Laino

the requested function is like below: $y = A\cos \left( {\frac{\pi }{k}} \right) + h$ where A is the amplitude, h is the vertical shift, and k is such taht the period of that function is: $T = \frac{{2\pi }}{k}$

3. Michele_Laino

that is the general formula, for your exercise

4. vera_ewing

So it's going to have to start out as f(x)= 3cos right?

5. Michele_Laino

yes!

6. vera_ewing

And the last part of the equation will be +2?

7. Michele_Laino

yes!

8. Michele_Laino

oops.. I have made a typo, here is the right formula: $y = A\cos \left( {\frac{x}{k}} \right) + h$

9. vera_ewing

f(x) = 3 cos 2x + 2 ?

10. Michele_Laino

yes! that's right!

11. vera_ewing

Thank you, Michele! :)

12. Michele_Laino

thanks! :)