What are the angles that would satisfy the following trigonometric equation below, ranging from 0 degree to 360 degrees?

#6 cosx - 5sinx = 0#

1 Answer
Apr 1, 2018

The solutions are #x=arctan(6/5),quad180^@+arctan(6/5)#.

Explanation:

#6cosx-5sinx=0#

#6cosx=5sinx#

Divide by #cosx#:

#(6cosx)/cosx=(5sinx)/cosx#

#(6color(red)cancelcolor(black)cosx)/color(red)cancelcolor(black)cosx=(5sinx)/cosx#

#6=(5sinx)/cosx#

#6=5*sinx/cosx#

#6=5*tanx#

#6/5=(5*tanx)/5#

#6/5=(color(red)cancelcolor(black)5*tanx)/color(red)cancelcolor(black)5#

#6/5=tanx#

#tanx=6/5#

#x=arctan(6/5),quad180^@+arctan(6/5)#

#color(white)x~~50.1944^@,230.1944^@#

The reason there are two answers is that the #tan# function is periodic every #180^@#, so we can add #180^@# and the answer will still be between #0^@# and #360^@#.

Hope this helped!