An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate

Question

3tan(3θ) − 1 = 0

Answer 1

square both sides

3tan3x = 1

tan3x = 1/3

use the inverse trig function on a calculator

3x = 18.435 degrees

x = 6.145 degrees + or -180k

x=6.145, 186.145, 366.145, ... degrees

also

x=6.145-180, 6.145-360, ....

= 173.855, 353.855, .... degrees

there are an infinite number of solutions, all in the 1st and 3rd quadrants