Advanced Trigonometry, SMB-042 Find all the values of \(\theta\), where \(-180^{\circ} \leq \theta \leq 180^{\circ}\), such that \(\tan\,\theta(\tan\,\theta-1)=0\) (3 marks) --- 6 WORK AREA LINES (style=lined) --- Show Answers Only \(\theta=-180^{\circ}, -135^{\circ}, 0^{\circ}, 45^{\circ}, 180^{\circ}\) Show Worked Solution \(\text{If}\ \ \tan\,\theta=0\ \ \Rightarrow\ \ \theta=0^{\circ}, 180^{\circ}, -180^{\circ} \) \(\text{If}\ \ \tan\,\theta-1=0\ \ \Rightarrow\ \ \tan\,\theta=1\) \(\text{Reference angle:}\ \ \tan\,\theta=1\ \ \Rightarrow \ \ \theta = 45^{\circ}\) \(\text{tan is positive in 1st/3rd quadrants.}\) \(\theta=45^{\circ}, (180+45)^{\circ}=45^{\circ}, 225^{\circ} = 45^{\circ}, -135^{\circ}\ \ (-180^{\circ} \leq \theta \leq 180^{\circ}) \) \(\therefore \theta=-180^{\circ}, -135^{\circ}, 0^{\circ}, 45^{\circ}, 180^{\circ}\)