# How do you find the domain and range of y = sin(pi/3 - x)?

Jul 11, 2018

$\left(- \infty , \infty\right) \mathmr{and} \left[- 1 , 1\right]$

#### Explanation:

The domain for $y = a \sin \left(b x + c\right)$ is $x \in \left(- \infty , \infty\right)$m using

$\sin \left(a x + b + 2 k \pi\right) = \sin \left(a x + b\right) . , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

The range is $y \in \left[- a , a\right] .$, using $\left\mid \sin \right\mid \left(b x + c\right) \le 1$.

Illustrative ( not on uniform scale ) graph,

using $y = \sin \left(\frac{\pi}{3} - x\right)$, with range $\left[- 1 , 1\right]$:

graph{(y - sin (1.0347 - x ))(y-1)(y+1) = 0[-100 100 -10 10]}

Another illustration, with $y = - 4 \sin \left(- \frac{x}{2} + 5\right)$,

with range [ -4, 4 ]#:
graph{(y - 4 sin( x/2 - 5 ))(y-4)(y+4) = 0[-100 100 -10 10]}