Find the degree measures corresponding to the following radian measures (use `pi=(22)/7`). (i) `(11)/(16)` (ii) ` 4` (iii) `(5pi)/3` (iv) `(7pi)/6`

Options

A. `11/16`
B. `-4`
C. `(5pi)/(3)`
D. `(7pi)/(6)`

Explanation

i) `C=11/16`
`therefore D=180^(@)/pi xx C = 180^(@)/pi xx 11/16 = (180^(@) xx 11)/(22/7 xx 16)`
`=180^(@)/22 xx (11 xx 7)/(16) = 315^(@)/8`
`393/8^(@)=39^(@)(3/8 xx 60^('))`
`=39^(@)221/2^(') = 39^(@)22^(')30^('')`
Therefore, `11/16` radian `=39^(@)22^(')30^('')`. Ans.
ii) `C=-4`
`therefore D=(180^(@))/(pi) xx C = 180^(@)/(22/7) xx (-4) = (180^(@) xx (-4) xx 7)/(22)`
`=-2520/11 = -229(1/11 xx 60^(@))`
`-229^(@)5^(')27.27^(')`approx.
`=-229^(@) 5^(') 27.3^('')` approx.
Therefore, `-4` radian = `-229^(@)5^(')27.3^('')` approx. Ans.
iii) C`=(5pi)/(3)`
`therefore D=180^(@)/pi xx C= 180^(@)/pi xx (5pi)/(3) = 300^(@)`
Therefore `,(5pi)/(6)` radian =`300^(@)` Ans.
iv) `C=(7pi)/(6)`
`therefore D=180^(@)/pi xx C = 180^(@)/pi xx (7pi)/6 = 210^(@)`
Therefore, `(7pi)/(6)` radian `=210^(@)`. Ans.