Find the radian measure corresponding to the following degree measures:
(i) 300°
(ii) 35°
(iii) −56°
(iv) 135°
(v) −300°
(vi) 7° 30'
(vii) 125° 30'
(viii) −47° 30'

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Solution

$We have : 180 ° = π rad ∴ 1 ° = \frac{π}{180} rad$

$(i) 300 ° = (300 \times \frac{π}{180}) = \frac{5 π}{3} rad$

$(ii) 35 ° = 35 \times \frac{π}{180} = \frac{7 π}{36} rad$

$(iii) - 56 ° = - (56 \times \frac{π}{180}) = - \frac{14 π}{45} rad$

$(iv) 135 ° = 135 \times \frac{π}{180} = \frac{3 π}{4} rad$

$(v) - 300 ° = - (300 \times \frac{π}{180}) = - \frac{5 π}{3} rad$

$(vi) 30' = {(\frac{1}{2})}^{°} ∴ 7 ° 30' = {(7 \frac{1}{2})}^{°} = {(\frac{15}{2})}^{°} = \frac{15}{2} \times \frac{π}{180} = \frac{π}{24} rad$

$(vii) 30' = {(\frac{1}{2})}^{°} ∴ 125 ° 30' = {(125 \frac{1}{2})}^{°} = {(\frac{251}{2})}^{°} = \frac{251}{2} \times \frac{π}{180} = \frac{251 π}{360} rad$

$(viii) 30' = {(\frac{1}{2})}^{°} ∴ 47 ° 30' = - {(47 \frac{1}{2})}^{°} = - {(\frac{95}{2})}^{°} = - (\frac{95}{2} \times \frac{π}{180}) = - \frac{19 π}{72} rad$

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