Mathematics
OpenStudy (anonymous):

Find a solution for the attached equation...

OpenStudy (anonymous):

OpenStudy (anonymous):

ok.. this shouldn't be too bad...

OpenStudy (anonymous):

$\large \sin(a \pm b) = \sin(a)\cos(b) \pm \sin(b)\cos(a)$

OpenStudy (anonymous):

can you simplify this?

OpenStudy (anonymous):

what happened to the 3pi in the numerator?

OpenStudy (anonymous):

3pi... oops.. good eye...

OpenStudy (anonymous):

$\large \sin(x-\frac {3\pi}{4})=\sin(x)\cos(\frac {3\pi}{4})-\cos(x)\sin(\frac {3\pi}{4})$

OpenStudy (anonymous):

how would i go about simplifying something like that?

OpenStudy (anonymous):

$\large \sin(x+\frac {3\pi}{4})=\sin(x)\cos(\frac {3\pi}{4})+\cos(x)\sin(\frac {3\pi}{4})$

OpenStudy (anonymous):

do you know the unit circle?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

so what's cos(3pi/4) and sin(3pi/4)?

OpenStudy (anonymous):

im not sure how i would do that. i know what the unit circle is, but don't know how to apply it to this.

OpenStudy (anonymous):

ok.. 1 second...

OpenStudy (anonymous):

OpenStudy (anonymous):

ok.. those are with the angles in degrees... do you know their radian equivalents?

OpenStudy (anonymous):

no

OpenStudy (anonymous):

hmmm. that's why this doesn't look familiar..

OpenStudy (anonymous):

take a look at page 3... it's the same but with their radian equivalents... http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

OpenStudy (anonymous):

oh, that makes much more sense

OpenStudy (anonymous):

135 degrees is 3pi/4

OpenStudy (anonymous):

so i plug that into the equation instead of 3pi/4?

OpenStudy (anonymous):

so when we add.. $\large \sin(x-\frac {3\pi}{4}) +\sin(x+\frac {3\pi}{4})$

OpenStudy (anonymous):

well that is the same as 2cos(135/4)sinx...

OpenStudy (anonymous):

hang on violin.. i was afk

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

oh good... you already simplified.. but it's actually..

OpenStudy (anonymous):

2cos(135)sinx is that correct?

OpenStudy (anonymous):

so i don't need to keep the 4?

OpenStudy (anonymous):

no... 135 degrees = 3pi/4

OpenStudy (anonymous):

oh nevermind, i get it

OpenStudy (anonymous):

so according to the unit circle, what's cos(135 degrees) ?

OpenStudy (anonymous):

-sqrt2/2

OpenStudy (anonymous):

good... so...

OpenStudy (anonymous):

2cos(135)sinx = sqrt2 (this is your problem with the left side simplified) 2((-sqrt2)/2)sinx = sqrt2 -sqrt2 * sinx = 1 sinx = -1/sqrt2 sinx = -sqrt2/2

OpenStudy (anonymous):

i did the algebra all the way to the last line... tell me if you don't understand anything there...

OpenStudy (anonymous):

i get where you got that, but my choices are: x= pi/4 x= pi x= 3pi/2 x= 0 x= pi/2 how do i get my answer down to one of these?

OpenStudy (anonymous):

ok... those choices are in radians... think about your unit circle, the one with the degrees.. what angle gives you a sine of -sqrt2/2? (in degrees?)

OpenStudy (anonymous):

225

OpenStudy (anonymous):

what does 225 degrees correspond to in the unit circle with the radians?

OpenStudy (anonymous):

5pi/4

OpenStudy (anonymous):

but that's not one of your choices huh? lemme double check the work....

OpenStudy (anonymous):

ok... i found it...

OpenStudy (anonymous):

2cos(135)sinx = sqrt2 (this is your problem with the left side simplified) 2((-sqrt2)/2)sinx = sqrt2 -sqrt2 * sinx = sqrt2 sinx = -1 it was my algebra... sorry... :( that's correct now..

OpenStudy (anonymous):

what angle do you take the sine of to get -1?

OpenStudy (anonymous):

don't worry about it... you are helping me way too much for me to complain :)

OpenStudy (anonymous):

270, or 3pi/2!

OpenStudy (anonymous):

yep... :)

OpenStudy (anonymous):

thanks again for working the problem with me... :)

OpenStudy (anonymous):

Thanks for the help! I wish I could give you more than a medal haha