Question

Use a calculator to solve the equation on the interval [0,2pi].
sin3x=sinx
I'm not use how to do this. help!

Answer 1

the equation is this right?
\[\Large \sin(3x) = \sin(x)\]

Answer 2

Yup!

Answer 3

I just need to know how to do this problem on a calculator.

Answer 4

you have something like a TI 83 right?

Answer 5

IT-84

Answer 6

TI 84 you mean?

Answer 7

yes sorry.

Answer 8

that's fine

Answer 9

so the idea is that you can get everything to one side to get `sin(3x) - sin(x) = 0`

Answer 10

then you type `sin(3x) - sin(x)` into y1 of the graphing calculator

after you hit the `y=` key

then graph

Answer 11

you may have to adjust the window

Answer 12

ok. how do I adjust the window?

Answer 13

next to the `y=` key is the `window` key

Answer 14

then put in something like

xmin = -1
xmax = 7
ymin = -3
ymax = 3

Answer 15

I think an easy way to figure out the 0's is by making conjectures from the unit circle.
like we see that
sin(x)=sin(-x-pi)
and
that
sin(x)=sin(x+2npi)

So to solve something like
\[\sin(p x)=\sin(x) \\ \text{ I think the following two equations can give you all the solutions } \\ px=x+2n \pi \\ px=-x-\pi+2n \pi \\ \text{ I'm going to rewrite that bottom equation a little } \\ px=-x+\pi(2n-1)\]
then solve both equations for x.
\[px=x+2 n \pi \\ \text{ can be solved by first subtracting } x \text{ on both sides } \\ px-x= 2 n \pi \\ x(p-1)=2 n \pi \\ x=\frac{2 n \pi}{p-1} \text{ last step I divided both dies by } (p-1) \\ \text{ the other equation } px=-x+\pi(2n-1) \text{ can be solved in a similar way }\]

Answer 16

where n is an integer

Answer 17

ok so then my answers would be 0, 0.79, 2.36, 3.14, 3.93, and 5.50?

Answer 18

@freckles has a good way to solve it algebraically

yes you have the correct solutions @liefje8

see attached

Answer 19

Awesome, thank you very much!!

Answer 20

no problem