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
Posts: 16
Joined: Mon Jul 25, 2011 8:33 pm
Contact:

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

Postby sully039 » Fri Sep 16, 2011 10:25 pm

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?

User avatar
maggiemagnet
Posts: 315
Joined: Mon Dec 08, 2008 12:32 am
Contact:

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

Postby maggiemagnet » Sat Sep 17, 2011 12:32 am

sully039 wrote: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.

sully039 wrote: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.
:clap:


Return to “Trigonometry”