SOLUTION: Solve 3cos(x+40°) = 4sin(x+40°) for 0° ≤ x ≤ 360°

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Question 1190279: Solve 3cos(x+40°) = 4sin(x+40°) for 0° ≤ x ≤ 360°
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solve 3cos%28x%2B40%29+=+4sin%28x%2B40%29 for 0° ≤ x ≤ 360°

3cos%28x%2B40%29+=+4sin%28x%2B40%29

3%2F4=+sin%28x%2B40%29+%2Fcos%28x%2B40%29+

tan%28x%2B40%29+=3%2F4

x%2B40=tan%5E-1%283%2F4%29

x++=++tan%5E-1%283%2F4%29-40°

solutions:

x=tan%5E-1%283%2F4%29%2B180%2An-40°

for range 0° ≤ x ≤ 360°

radians:
x+=+%2816pi%29%2F9+%2B+2tan%5E%28-1%29%281%2F3%29
x+=+%2816pi%29%2F9+-+2tan%5E%28-1%29%281%2F3%29

degrees:
x=356.87°
x=283.13°



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve 3cos%28x%2B40%29+=+4sin%28x%2B40%29 for 0° ≤ x ≤ 360°
~~~~~~~~~~~~~~~~~~~~~~


            Below find the correct solution to replace the incorrect one from @MathLover1.


3cos%28x%2B40%29 = 4sin%28x%2B40%29

3%2F4 = sin%28x%2B40%5Eo%29+%2Fcos%28x%2B40%5Eo%29

tan%28x%2B40%29 = 3%2F4

x%2B40 = tan%5E%28-1%29%283%2F4%29

x = tan%5E%28-1%29%283%2F4%29-40°

solutions:

x = tan%5E-1%283%2F4%29-40+%2B+180%2An°

for range 0° ≤ x ≤ 360°

x%5B1%5D = 36.87-40%2B180° = 176.87°;
x%5B2%5D = 36.87-40%2B360° = 356.87°.

ANSWER.     Two solutions are   176.87°   and   356.87°   (both are approximate and rounded).


Solved.