SOLUTION: Dear tutor, How do I solve these trig equtions? I did not see a similar example on the suggested equitions here. Q1. 2cos(π/4x)+√3 =0 Q2. 4sin(π/4(x+2))+2 =0 Thank

Algebra ->  Trigonometry-basics -> SOLUTION: Dear tutor, How do I solve these trig equtions? I did not see a similar example on the suggested equitions here. Q1. 2cos(π/4x)+√3 =0 Q2. 4sin(π/4(x+2))+2 =0 Thank       Log On


   

Question 1196768: Dear tutor,
How do I solve these trig equtions? I did not see a similar example on the suggested equitions here.
Q1. 2cos(π/4x)+√3 =0
Q2. 4sin(π/4(x+2))+2 =0
Thank you so much.
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Q1.
2cos%28%28pi%2F4%29x%29%2Bsqrt%283%29+=0+
cos%28%28pi%2F4%29x%29+=-sqrt%283%29%2F2
%28pi%2F4%29x=cos%5E-1%28-sqrt%283%29%2F2%29
%28pi%2F4%29x=%285+%2F6%29pi
x=%285pi+%2F6%29%2F%28pi%2F4%29
x+=+10%2F3
general solutions:
x+=+8n+-+10%2F3,+n element Z
x+=+8n+%2B14%2F3, n+element Z

Q2.
4sin%28%28pi%2F4%29%28x%2B2%29%29%2B2+=0
sin%28%28pi%2F4%29%28x%2B2%29%29+=-2%2F4
sin%28%28pi%2F4%29%28x%2B2%29%29+=-1%2F2
%28pi%2F4%29%28x%2B2%29+=sin%5E-1%28-1%2F2%29
%28pi%2F4%29%28x%2B2%29+=-pi%2F6
%28x%2B2%29+=%28-pi%2F6%29%2F%28pi%2F4%29
x%2B2+=-2%2F3
x+=-2%2F3-2
x+=-8%2F3
general solutions:
x=8n%2B8%2F3,+n element Z
x=8n%2B16%2F3,+n element Z

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
 Q1. 2cos(π/4x)+√3 =0 
0r cos(π/4x) = -√3/2 
  | See wheel below (cosx, sinx)  
   cos(5π/6) = -√3/2   
      5pi%2F6+=++pi%2F4x    |Cross multiply and solve for x
      20πx = 6π
         x = 6/20 = 3/10

Q2. 4sin(π/4(x+2))+2 =0   0r sin (π/4(x+2)) = -2/4 = -1/2 
Look on Wheel:   sin (7π/6) = -1/2
%28pi%2F4%28x%2B2%29%29+=+7pi%2F6  |Cross multiply and solve for x 
 .
Wish You the Best.