Please I need a help in this Q Write a sine function and a cosine function which match the following graph. Note that the x-axis goes from 0 to 2 pi and the y-axis goes from -7 to 8. Solution sine function peak to peak = 8 so one peak = 4 it\'s shifted 2 units downward , and the period is 2pi/2 = pi f(x) = 4 sin(2x) - 2 cosine like sine but shifted right by (pi / 4) f(x) = 4 cos 2(x - pi/4) - 2 => f(x) = 4 cos (2x - pi/2) - 2.

1. Please I need a help in this Q Write a sine function and a cosine function which match the
following graph. Note that the x-axis goes from 0 to 2 pi and the y-axis goes from -7 to 8.
Solution
sine function
peak to peak = 8 so one peak = 4
it's shifted 2 units downward , and the period is 2pi/2 = pi
f(x) = 4 sin(2x) - 2
cosine
like sine but shifted right by (pi / 4)
f(x) = 4 cos 2(x - pi/4) - 2
=> f(x) = 4 cos (2x - pi/2) - 2