What is the shift f(x)=8cos(2x-30)+7 ?

The shift f(x)=8cos(2x-30)+7 is Phase: pi/(12), Vertical:7

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shift f(x)=8cos(2x-30)+7

shift

f (x) = 8 cos (2 x - 3 0^{\circ}) + 7

Phase : \frac{π}{12}, Vertical : 7

Solution steps

Convert

30

degrees to radians:

\frac{π}{6}

8 cos (2 x - \frac{π}{6}) + 7

f (x) = 8 cos (2 x - \frac{π}{6}) + 7

g (B x - C) = cos (2 x - \frac{π}{6}), B = 2, C = \frac{π}{6}, D = 7

Therefore, the phase shift

\frac{C}{B}

\frac{\frac{π}{6}}{2}

\frac{π}{12}

The vertical shift

D

7

7

What is the shift f(x)=8cos(2x-30)+7 ?
The shift f(x)=8cos(2x-30)+7 is Phase: pi/(12), Vertical:7