# How do you use the amplitude and period to graph y = –3 cos(2θ + 45°) + 3 ?

Apr 30, 2016

Amplitude 3, period $\pi$

#### Explanation:

General form of a sinusoidal (or sine wave) function is$y = A \sin \left(B x - C\right) + D$
Where |A| is the amplitude, period is $\frac{2 \pi}{B}$ Phase shift is $\frac{C}{B}$ and D is the vertical shift.
Now in the given function instead of sine it is cos. Hence we change it by wrting cosx as $\sin \left(x + \frac{\pi}{2}\right)$

The given function can thus be written as $y = - 3 \sin \left(2 \theta + {45}^{o} + {90}^{o}\right) + 3$
0r $y = - 3 \sin \left(2 \theta + \frac{3 \pi}{4}\right) + 3$

Thus amplitude would be 3 and period would be $\frac{2 \pi}{2}$ or, $\pi$