Domain & range of trig function

**fezz349** · September 8th 2009, 09:23 AM

need some help with this one guys..

y=2sin(3x + pi) -1

**red_dog** · September 8th 2009, 09:36 AM

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 $[-3,1]$

**fezz349** · September 8th 2009, 09:50 AM

thanks a lot bro, btw, does the R in the domain mean all rea numbers?

**TKHunny** · September 8th 2009, 02:05 PM

You got it. The fancy "R" does, indeed, mean The Real Numbers. Guess what a fancy "N" means?

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