Question

2. Determine an equation for a cosine function that has a period of 1800°, an amplitude of 3, a

vertical shaft of 4, and a phase shift of 225° right.

Answer 1

`y=3cos((1)/(2) (x+}225)+4` phase shift in degrees

`y=3cos((1)/(2) (x+(5\pi )/(4)))+4` phase shift in pi radians

Explanation:

Here is the equation for the graph of the cosine function.

y = A sin(B(x + C)) + D

A = amplitude

period is 2π/B

C = phase shift

D = vertical shift

Lets convert 1800° to Pi radians.

`1800*(\pi )/(180)`

`180(10)*(\pi )/(180)`

`10*(\pi )/(180)`

`10\pi` radians

A = 3

B=2π/ 10π simplifies to
`(1)/(2)`

C = phase shift

D = 4

`y=3cos((1)/(2) (x+}225)+4` phase shift in degrees

`y=3cos((1)/(2) (x+(5\pi )/(4)))+4` phase shift in pi radians