## how many solns does 5sinx = 2 have on 0 < x < 4pi ?

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
sully039
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### how many solns does 5sinx = 2 have on 0 < x < 4pi ?

How many solutions are there to the equation 5sinx=2 for the domain 0<x<4pi?
(5sinx)/5=2/5
sinx=2/3
sin-1(2/5)=23.5781

So does this mean there is only one solution to this equation?
If not, how do I find the other answers?

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: how many solns does 5sinx = 2 have on 0 < x < 4pi ?

How many solutions are there to the equation 5sinx=2 for the domain 0<x<4pi?
(5sinx)/5=2/5
sinx=2/3
sin-1(2/5)=23.5781

So does this mean there is only one solution to this equation?
No; it means that the primary solution, given by the inverse function, is approximately 23.5781.
If not, how do I find the other answers?
Use what you know about graphing sine to find the other places where the graph is at the same height as for the primary solution. Then use symmetry to find the "exact" values by adding or subtracting 23.5781 from 0, pi, 2pi, etc.