Find \( sin \theta \) and \( cos \theta \) , given that \( tan \theta= \frac{3}{4}\) and \( \theta \) is acute.

By Pythagoras' Theorem

4 3 5 θ

Therefore \( sin \theta= \frac{3}{5} \) and \( cos \theta= \frac{4}{5} \)

Find \( sin \theta \) and \( tan \theta \) , given that \( cos \theta= -\frac{12}{13}\) and \( \theta \) is obtuse.

By Pythagoras' Theorem

12 5 13 θ

Therefore in the second quadrant (i.e where \( \theta\) is obtuse), \( sin \theta= \frac{5}{13} \) and \( tan \theta= -\frac{5}{12} \)

Find \( tan \theta \) and \( cos \theta \) , given that \( sin \theta= -\frac{\sqrt3}{2}\) and \( \theta\) is reflex.

By Pythagoras' Theorem

1 √3 2 θ

Therefore in the third quadrant (i.e where \( \theta\) is reflex), \( tan \theta= \frac{\sqrt{3}}{1} \) and \( cos \theta= -\frac{1}{2} \)