a sinusoidal function has amplitude 3, period pi, a maximum at (pi/4, 5) and a minimum at (3pi/4, -1).

Question

a sinusoidal function has amplitude 3, period pi, a maximum at (pi/4, 5) and a minimum at (3pi/4, -1): a) represent a function with an equation using a sine function. b) represent a function with an equation using a cosine function.

Answer 1

The amplitude is 3.

The vertical shift is 5-3= 2.

The period is pi, so we need 2pi/pi = 2 as the coefficient of x.

The min and max will occur at pi/2 and 3pi/2 normally. If the period is pi, then pi/4 and 3pi/4 will be our new maxs and mins.

So use f(x) = 3sin(2x) + 2

☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆

The cosine function is 90 ahead of the sine function if its period is 2pi, and 45 degrees ahead if the period is pi. So subtract pi/4 from the phase shift and replace sine with cosine.

f(x) = 3cos(2(x-(pi/4))) + 2

The functions now graph identically.