Find the points of intersection of each pair of curves in the given interval.
i) y=sin2x, y=sinx

Question

Find the points of intersection of each pair of curves in the given interval.
i) y=sin2x, y=sinx

anonymous · Answer

set the y's equal...:
sin2x = sinx                     given
2sinxcosx = sinx            use the double angle formula for sine
2sinxcosx - sinx = 0      move the sinx over to the left side
sinx(2cosx - 1) = 0         factor

can you do the rest from here?

anonymous · Answer

and btw,  what is the interval?

anonymous · Answer

$$(0 \pm 2*\pi*n,0),(\pi \pm 2*\pi*n,0)$$

anonymous · Answer

I got 0,0 but theres more intervals that icant get

anonymous · Answer

no... what interval do you want to look for solution(s)?  as it is stated in the problem, "... in the given interval"

anonymous · Answer

what is the given interval?

anonymous · Answer

SOrry the given interval is 0

anonymous · Answer

ok... the interval is [0, 2pi]

anonymous · Answer

so from the last equation:  sinx(2cosx - 1) = 0
you'll need to set each factor equal to zero...
sinx = 0        solve this...

and also

2cosx - 1 = 0    solve this....

anonymous · Answer

in the first equation, what angle between 0 and 2pi will give you a sine of zero?