exercises xxx involve equations with multiple angles . solve each equation on the interval [0, 2pi)

28) sin 4x= - radical 2 / 2

I was told to let 4x = u so I have

sin u = - radical 2 /2 ( 5pi/4)

set 4x = 5pi/4 divide by 4 and get

x = 5pi/16

which I don't totally understand but ok... "Then let u = 7pi/4 x then would 7pi/16"

can someone explain this to me in any better terms...

simply put, you're solving 2 different problems

it's sin( something) = -sqrt(2)/2

"something" must be 5pi/4 or 7pi/4 on the given interval

that you should understand

"something" is equal to 4x in your case
and you're solving for x

4 times x must = 5pi/4 and 4 times x =7pi/4

This post was edited by saber_x3 on Apr 6 2014 01:32pm

ok I think I understand.. the converting to u and back to 4x and stuff was confusing me.

so I have 4x = 5pi/4 and 4x = 7pi/4 because the unit circle gives those points for -radical 2/2

so 4x= 5pi/4
x = 5pi/16

and 4x = 7pi/4
x = 7pi/16

7pi/16 and 5pi/16 are my solutions

also the "solve each equation on the interval 0, 2pi" was confusing too what does this mean?

This post was edited by fingerling on Apr 6 2014 01:41pm

that has to do with the unit circle
it's 360 degress , 2pi, for the whole circle
however the circle repeats infinitely, so there is more than just the answers you get on the interval of 0 to 2pi