# How do you sketch the graph of y=2 - sin ((2πx)/3)?

Jul 27, 2018

See graph and details.

#### Explanation:

$y = 2 - \sin \left(\frac{2 \pi x}{3}\right) \in \left(2 , 2\right) + \left(- 1 , 1\right) = \left(1 , 3\right)$

Amplitude of this sine wave $= \left\mid - 1 \right\mid = 1$.

Period = ( 2pi )/((2pi)/3) = 3#

Now see the wave,, with these depicted thereupon, for one period

$x \in \left[- 1.5 , 1.5\right]$:

graph{(y-2+sin(2/3pix))(y-1)(y-2)(y-3)(x^2-2.25)=0[-4 4 0 4]}

Observe axis of the wave $y = 2$.