# Domain & range of trig function

• September 8th 2009, 10:23 AM
fezz349
Domain & range of trig function
need some help with this one guys..

y=2sin(3x + pi) -1
• September 8th 2009, 10:36 AM
red_dog
First of all use the formula $\sin(\pi+x)=-\sin x$.

Then $y=-2\sin 3x-1$

The domain is $\mathbb{R}$.

We have $-1\leq\sin 3x\leq 1\Rightarrow -2\leq -2\sin 3x\leq 2\Rightarrow -3\leq -2\sin 3x-1\leq 1$

So the range is $[-3,1]$
• September 8th 2009, 10:50 AM
fezz349
thanks a lot bro, btw, does the R in the domain mean all rea numbers?
• September 8th 2009, 03:05 PM
TKHunny
You got it. The fancy "R" does, indeed, mean The Real Numbers. Guess what a fancy "N" means?