Question

What is the general equation of a sine function with an amplitude of 6, a period of... and a horizontal shift of...?

Answer 1

Step-by-step explanation:

I think I'm a little too late to answer this question, but I'm still going to give you a basic sin function to show you where to find these things :)

$f(x)=a sin (px)+s$

I put the variables corresponding to their appropriate word.

(a=amplitude, p=period, s=shift)

You can find the amplitude in front of the sin (or cos, tan, cot, etc). The amplitude is always the first number presented in a trig function.

You find the period by taking the number paired with the x and dividing 2π by it. ( $\frac{2\pi }{p}$ ) In this case, you're looking for a period of $\frac{\pi }{4}$ which means that you would be dividing the 2π by 8 ($\frac{2\pi }{8} =\frac{\pi }{4}$ )

The shift is always added at the end of the function.

- For vertical shifts, the shift is added separately as it's own individual value. (A good example would be the last option in your sc; $y=6sin(8x)+\frac{\pi }{2}$).

- For horizontal shift, the shift is joined with the x in the parentheses. If you want to think about it this way, the horizontal axis is the x-axis. Therefore, it makes sense that if it's a horizontal shift, the shift will be with the x.

Using all this information, we can determine that the answer has to have a 6 in front of it, an 8 multiplied with the x, and a $\frac{\pi }{2}$ in parentheses with the x.

Your final answer should be the 3rd option, $y=6sin(8(x-\frac{\pi }{2} ))$

Answer:

$y=6sin(8(x-\frac{\pi }{2} ))$