Solution:

We know that π rad = 180°

Or, we can write: 1 rad = 180°/ π

(iii) (18π/5)

Making use of the above relation, we can write => [(180/π) × (18π/5)] ^o

Putting the value of π = 22/7

$ =\left[ 180/22\text{ }\times \text{ }7\text{ }\times \text{ }18\text{ }\times \text{ }22/\left( 7\times 5 \right) \right] $

$ =\left( 36\text{ }\times \text{ }18 \right)\text{ }{}^\circ  $

$ =648{}^\circ  $

Therefore, the degree measure of 18π/5 is 648°

(iv) (-3) ^c 

Making use of the above relation, we can write => [(180/π) × (-3)] ^o

Putting the value of π = 22/7

$ {{\left[ 180/22\text{ }\times \text{ }7\text{ }\times -3 \right]}^{o}} $

$ ={{\left( -3780/22 \right)}^{o}} $

$ =\left( -{{171}^{~o~}}\left( 18/22\text{ }\times \text{ }60 \right)’ \right) $

$ =\left( -{{171}^{o}}~\left( 49\text{ }1/11 \right)’ \right) $

$ =\left( -{{171}^{o}}~49’\text{ }\left( 1/11\text{ }\times \text{ }60 \right)’ \right) $

$ =-\left( 171{}^\circ \text{ }49’\text{ }5.45” \right) $

$ \approx -\left( 171{}^\circ \text{ }49’\text{ }5” \right) $

Therefore, the degree measure of (-3) ^c is -171° 49′ 5”