Trigonometric equations

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Consider the equation $\tan x = \tan(85^{\circ})$. Its general solution is $x = 85^{\circ} + 180^{\circ} n$ for an integer $n$. Find the solution (in degrees) that lies in the interval $[720^{\circ}, 900^{\circ})$.

2. Warm-up

   Consider the equation $\tan x = \tan(55^{\circ})$. Its general solution is $x = 55^{\circ} + 180^{\circ} n$ for an integer $n$. Find the solution (in degrees) that lies in the interval $[540^{\circ}, 720^{\circ})$.

3. Warm-up

   Consider the equation $\tan x = \tan(165^{\circ})$. Its general solution is $x = 165^{\circ} + 180^{\circ} n$ for an integer $n$. Find the solution (in degrees) that lies in the interval $[720^{\circ}, 900^{\circ})$.

Problems shown under their original terms: Generated (template, solver-computed).