a. 

\(\text{Draw a horizontal line on graph from}\ \ \cos\,\theta=0.3:\)
 

\(\theta \approx 75^{\circ}, 285^{\circ}\)
 

b.   \(\cos\,300^{\circ}\ \text{is in the 4th quadrant.}\)

\(\text{Reference angle:}\ \theta=360-300=60^{\circ}\)

\(\Rightarrow \ \cos\,300^{\circ} = \cos\,60^{\circ} \)

\(\sin\,50^{\circ} = \cos(90-50)^{\circ} = \cos\,40^{\circ}\)
 

\(\text{Graphically, it can be seen that}\ \ \cos 60^{\circ} \lt \cos\,40^{\circ}\)

\(\Rightarrow\ \cos 300^{\circ} \lt \sin\,50^{\circ}\)

\(\therefore \ \text{Statement is not correct.}\)

a.   \(\text{Drawing a horizontal line from 0.4 on the \(y\)-axis:}\)
 

\(\therefore \theta \approx 25^{\circ}, 155^{\circ}\)
 

b.   \(\text{Drawing a horizontal line from –0.6 on the \(y\)-axis:}\)
 

\(\therefore \theta \approx 325^{\circ}\)

a.  \(\theta \approx 125^{\circ}, 235^{\circ}\)
 

b.   \(\sin\,155^{\circ}\ \text{is in the 2nd quadrant.}\)

\(\text{Reference angle:}\ \theta=180-155=25^{\circ}\)

\(\sin\,25^{\circ} =\cos(90-25)^{\circ}=\cos\,65^{\circ}\)
 

\(\text{Graphically, it is shown}\ \ \cos 60^{\circ} \lt \sin 155^{\circ} (\cos\,65^{\circ})\)

\(\therefore \ \text{Statement is not correct.}\)

a.    \(\sin\,50^{\circ} \approx 0.8\)

b.   \(\cos\,20^{\circ}=\sin(90-20)^{\circ}=\sin\,70^{\circ}\)
 

\(\text{Graphically, it can be seen that}\ \ \cos 20^{\circ}\ (\sin\,70^{\circ}) \gt \sin 50^{\circ}\)

\(\therefore \ \text{Statement is correct.}\)