Advanced Trigonometry, SMB-035

Solve for all \(\theta\) in the range \(0^{\circ} \leq \theta \leq 360^{\circ}\), that make the following equation correct

\(\cos^{2}\theta-\cos\,\theta=0\) (3 marks)

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\(\theta=0^{\circ},90^{\circ},270^{\circ},360^{\circ}\)

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\(\cos^{2}\theta-\cos\,\theta\)	\(=0\)
\(\cos\,\theta(\cos\,\theta-1)\)	\(=0\)

\(\text{If}\ \ \cos\,\theta=0\ \ \Rightarrow\ \ \theta=90^{\circ}, 270^{\circ}\)

\(\text{If}\ \ \cos\,\theta-1=0\ \ \Rightarrow\ \ \cos\,\theta=1\ \ \Rightarrow\ \ \theta=0^{\circ}, 360^{\circ}\)

\(\theta=0^{\circ},90^{\circ},270^{\circ},360^{\circ}\)