# How do you find the amplitude, period, vertical and phase shift and graph y=sintheta+0.25?

Jul 26, 2018

Below

#### Explanation:

$y = \sin \theta + 0.25$ can also be written as $y = 0.25 + \sin \theta$ which is in the form $y = b + a \sin \left(n \theta\right)$
where $a$ is the amplitude and $b$ is the shift upwards or downwards and $n$ is the phase shift

Now when we compared $y = 0.25 + \sin \theta$ and $y = b + a \sin \left(n \theta\right)$, we can say that:

$b = 0.25$
$a = 1$
$p e r i o d \left(T\right) = \frac{2 \pi}{n} = \frac{2 \pi}{1} = 2 \pi$

Therefore, we know that $y = \sin \theta + 0.25$ is the graph $y = \sin \theta$ shifted UPWARDS by $0.25$ units and they also have the same phase shift $\left(2 \pi\right)$

Below is graph $y = \sin \theta$

graph{sinx [-10, 10, -5, 5]}

Below is graph $y = \sin \theta + 0.25$

graph{0.25+sinx [-10, 10, -5, 5]}