Question

Find a solution for the attached equation...

Answer 1

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

Answer 2

\[\large \sin(a \pm b) = \sin(a)\cos(b) \pm \sin(b)\cos(a)\]

Answer 3

can you simplify this?

Answer 4

what happened to the 3pi in the numerator?

Answer 5

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

Answer 6

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

Answer 7

how would i go about simplifying something like that?

Answer 8

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

Answer 9

do you know the unit circle?

Answer 10

yes

Answer 11

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

Answer 12

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.

Answer 13

ok.. 1 second...

Answer 14

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

Answer 15

no

Answer 16

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

Answer 17

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

Answer 18

oh, that makes much more sense

Answer 19

135 degrees is 3pi/4

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

hang on violin.. i was afk

Answer 24

ok

Answer 25

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

Answer 26

2cos(135)sinx
is that correct?

Answer 27

so i don't need to keep the 4?

Answer 28

no...
135 degrees = 3pi/4

Answer 29

oh nevermind, i get it

Answer 30

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

Answer 31

-sqrt2/2

Answer 32

good...
so...

Answer 33

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

Answer 34

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

Answer 35

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?

Answer 36

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?)

Answer 37

225

Answer 38

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

Answer 39

5pi/4

Answer 40

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

Answer 41

ok... i found it...

Answer 42

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..

Answer 43

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

Answer 44

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

Answer 45

270, or 3pi/2!

Answer 46

yep... :)

Answer 47

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

Answer 48

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