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

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Answer 1 · 2018-07-11T13:54:52

#(- oo, oo ) and [ - 1, 1 ]#

The domain for #y = a sin ( b x + c )# is #x in ( - oo, oo )#m using

#sin ( a x + b + 2 k pi ) = sin (ax + b )., k = 0, +- 1, +-2, +-3,...#

The range is # y in [ - a, a ].#, using #abs sin ( b x +c ) <= 1#.

Illustrative ( not on uniform scale ) graph,

using #y = sin ( pi/3 - x )#, with range #[ - 1, 1 ]#:

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

Another illustration, with # y = -4 sin (- x / 2 + 5 )#,

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