a.   \(175^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (sin +ve/cos –ve)} \)

\(\text{Reference angle:}\ 180-175=5^{\circ}\)

\(\tan 175^{\circ} = \dfrac{\sin 5^{\circ}}{-\cos 5^{\circ}} = -\tan 5^{\circ}\)
 

b.   \(262^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180+\theta=262^{\circ}\ \ \Rightarrow\ \ \theta=82^{\circ}\)

\(\cos 262^{\circ} = -\cos 82^{\circ}\)

a.   \(140^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180-140=40^{\circ}\)

\(\cos 140^{\circ} = -\cos 40^{\circ}\)

b.   \(345^{\circ}\ \ \Rightarrow\ \ \text{4th quadrant (sin –ve/cos +ve)} \)

\(\text{Reference angle:}\ 360-345=15^{\circ}\ \ \Rightarrow \ \theta=15^{\circ}\)

\(\tan 345^{\circ} = \dfrac{-\sin 15^{\circ}}{\cos 15^{\circ}} = -\tan 15^{\circ}\)

a.   \(235^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (sin/cos –ve)} \)

\(\text{Reference angle:}\ 180+\theta=235^{\circ}\ \ \Rightarrow \ \theta=55^{\circ}\)

\(\tan 235^{\circ} = \dfrac{-\sin 55^{\circ}}{-\cos 55^{\circ}} = \tan 55^{\circ}\)

b.   \(310^{\circ}\ \ \Rightarrow\ \ \text{4th quadrant (sin –ve)} \)

\(\text{Reference angle:}\ \ 360-310=50^{\circ}\)

\(\sin 310^{\circ} = -\sin 50^{\circ}\)

a.   \(165^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (sin +ve)} \)

\(\text{Reference angle:}\ \ 180-165=15^{\circ}\)

\(\sin 165^{\circ} = \sin 15^{\circ}\)

b.   \(250^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180+\theta=250^{\circ}\ \ \Rightarrow \ \theta=70^{\circ}\)

\(\cos 250^{\circ} = -\cos 70^{\circ}\)