Write the equation for the graph above Show all calculations

Write the equation for the graph above. Show all calculations for y = d + a sin(bx - c) Simplify: sec theta - sin theta tan theta using basic identities angle A in QII, sin A = 4/5, angle B in QI, cos B = 5/13, Find sin(A + B)

Solution

y = d + asin(bx -c)

max, = 4 ; min. = -2

midlevel = 1

amplitude = 3

period = pi ; b = 2pi/pi = 2

y = 1 +3sin(2x -c)

we are given y interecpt : x= 0 ; y =1 .Find c from this information:

1 = 1 +3sin(-c)

0 = sin(-c)

c = pi

So, y = 1 +3sin(2x - pi)