Find the range of the function f(t) = 2sinθ.

How would I do this problem?

Thanks for your help!

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- Jan 18th 2009, 01:01 PMlive_laugh_luv27Sine function
Find the range of the function f(t) = 2sinθ.

How would I do this problem?

Thanks for your help! - Jan 18th 2009, 01:26 PMMush
- Jan 18th 2009, 02:09 PMlive_laugh_luv27
- Jan 18th 2009, 02:42 PMMush
That doesn't make sense to me.

Are you sure it's not:

$\displaystyle f(t) = 2\sin(t) $

or

$\displaystyle f(\theta) = 2\sin(\theta) $

??

In any case, the range of a function, is the range of values of $\displaystyle f(t) $ or $\displaystyle f(\theta) $ that emerge as $\displaystyle t $ or $\displaystyle \theta $ vary across their domain.

Your function is a sine wave, hence $\displaystyle t $ or $\displaystyle \theta $ vary from $\displaystyle -\infty $ and $\displaystyle \infty $. $\displaystyle f(t) $ or $\displaystyle f(\theta) $, a sine wave ranges between positive and negative its amplitude. Do you know what the amplitude of your sinewave is? Let the amplitude be $\displaystyle a $.

Hence the range is

$\displaystyle -a \leq f(t) \leq a $

or

$\displaystyle -a \leq f(\theta) \leq a $

But what is a? That's the bit you have to do!

Depending on which was meant. Unless your equation is actually correct and there's an extra element to this question that I don't understand.