Determine the angle \( \theta \) which will maximise the moment \( M O \) of the 200 N force about the shaft axis at \( O \). Also compute \( M O \).

Given that \( \tan 75^{\circ}=2+\sqrt{3} \) hence determine \( \tan 15^{\circ} \) leaving your answer in the form \( a+b \sqrt{c} \)

Nite the expression below in surd form and rationalize the denominator \[ \frac{1-\cos 60^{\circ}}{1+\operatorname{tim} 30^{\circ}} \]

Solve \( 8 \sin \left(\frac{\pi}{5} x\right)=4 \) for the four smallest positive solutions

When evaluating the expression \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \), the angle obtained is ...

Solve \( \sin ^{2}(t)=-8 \cos (t) \) for all solutions \( 0 \leq t<2 \pi \)