Trigonometric equations with multiple angles

[ariannadimartino]

Hi guys
what is the logic behind the expressions i highlighted?
I just don’t understand
thank you

[HallsofIvy]

The first problem species that x is from 0 to 360. So 3x- 20 is between 3(0)- 20= -20 and 3(360)- 20= 1080- 20= 1060 The tangent function is periodic with period 180 degrees so in addition to 50.036 degrees we get other values of the function by repeatedly adding 180 to that and recalculating x from that.