Solve \(sin3 \theta = 0.71 \) in the interval \(0^{\circ} \leqslant \theta \leqslant 360^{\circ}\)

(solutions to 2 d.p.)

Our modified interval is \(0^{\circ} \leqslant 3 \theta \leqslant 1080^{\circ}\)

\begin{align} \\ and\ we\ know \\ \\ sin^{-1}(0.71)= 3 \theta \\ \\ So \quad3 \theta= 45.235^{\circ}, \, 134.765^{\circ}, \, 405.235^{\circ}, \\ \quad \quad 494.765^{\circ}, \, 765.235^{\circ}, \, 854.765^{\circ} \\ \\ And \quad \theta=15.08^{\circ}, \, 44.92^{\circ}, \, 135.08^{\circ}, \\ \quad 164.92^{\circ}, \, 255.08^{\circ}, \, 284.92^{\circ} \\ \end{align}

Solve \(cos2 \theta = 0.36 \) in the interval \(0^{\circ} \leqslant \theta \leqslant 360^{\circ}\)

(solutions to 2 d.p.)

Our modified interval is \(0^{\circ} \leqslant 2 \theta \leqslant 720^{\circ}\)

\begin{align} \\ and\ we\ know \\ \\ cos^{-1}(0.36)= 2 \theta \\ \\ So \quad 2 \theta= 68.899^{\circ}, \, 291.101^{\circ}, \, 428.899^{\circ}, \\ \quad \quad 651.101^{\circ} \\ \\ And \quad \theta=34.45^{\circ}, \, 145.55^{\circ}, \, 214.45^{\circ}, \\ \quad 325.55^{\circ} \\ \end{align}