SOLUTION: Hi. I've been trying to solve this trig. equation 4sin4t + 3cos4t = 0. The answer is meant to be t = {{{pi/4 - 1/4 * arctan(3/4)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Hi. I've been trying to solve this trig. equation 4sin4t + 3cos4t = 0. The answer is meant to be t = {{{pi/4 - 1/4 * arctan(3/4)}}}       Log On


   

Question 300382: Hi. I've been trying to solve this trig. equation 4sin4t + 3cos4t = 0. The answer is meant to be t = pi%2F4+-+1%2F4+%2A+arctan%283%2F4%29
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
4sin%284t%29+%2B+3cos%284t%29+=+0
4sin%284t%29+=-3cos%284t%29
sin%284t%29%2Fcos%284t%29=-3%2F4
tan%284t%29=-3%2F4
4t=arctan%28-3%2F4%29%2B+pi
t=arctan%28-3%2F4%29%2F4+%2B+pi%2F4
You can also bring out the negative sign from the arctan argument since
tan%28-x%29=-tan%28x%29
t=-arctan%283%2F4%29%2F4+%2B+pi%2F4
t=pi%2F4-arctan%283%2F4%29%2F4+