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Solve Linear Trig Equations

  1. Nov 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Solve sin (x + pi/4) = √2 cos x

    2. Relevant equations


    3. The attempt at a solution
    sinx*cos(pi/4) + cosx*sin(pi/4) = √2 cos x
    √2/2 sinx + √2/2 cosx = √2 cos x
    not sure if im on the right track? or where would I go from here? would I bring √2 cos x to the left side?
     
  2. jcsd
  3. Nov 24, 2016 #2

    LCKurtz

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    I would note that ##\frac {\sqrt 2} 2 = \frac 1 {\sqrt 2}## and multiply both sides by ##\sqrt 2##.
     
  4. Nov 24, 2016 #3
    Did that now I'm left with (sinx + cosx) = 2cosx, I'm stuck now? Tried bringing to other side and does not work and tried cancelling out the cosx but that does not work.
     
  5. Nov 24, 2016 #4

    LCKurtz

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    Show us what you get when you simplify it. Telling us it didn't work doesn't help us help you when we don't know what you did.
     
  6. Nov 24, 2016 #5

    lurflurf

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    just use the identity
    $$\sin\left(x+\frac{\pi}{4}\right)=\sin\left(x-\frac{\pi}{4}\right)+\sqrt{2}\cos(x)$$
    or equivalently
    $$\sin\left(x+\frac{\pi}{4}\right)-\sin\left(x-\frac{\pi}{4}\right)=\sqrt{2}\cos(x)$$
     
  7. Nov 24, 2016 #6
    Lol I got the answer.

    (sinx + cosx)/cosx = (2cosx)/cosx

    Now I am left with

    (sinx/cosx) + 1 = 2

    sinx/cosx = 2-1

    tanx = 1

    x = tan-1(1)

    x = pi/4

    or

    x = pi + pi/4 = 5pi/4
     
  8. Nov 24, 2016 #7

    LCKurtz

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    How about angles coterminal with those?
     
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