Q.Convert the following angles into radian.

Step 1: Use $\theta° = \theta\times\frac{\pi}{180}$ radian, simplifying the fraction each time. For the D-M measures, first write the minutes as a decimal degree ($30'=0.5°$, $48'=0.8°$).

i) $85° = 85\times\frac{\pi}{180} = \frac{17\pi}{36}$ (dividing by $5$).

ii) $250° = 250\times\frac{\pi}{180} = \frac{25\pi}{18}$ (dividing by $10$).

iii) $-132° = -132\times\frac{\pi}{180} = -\frac{11\pi}{15}$ (dividing by $12$).

iv) $65°30' = 65.5° = \frac{131}{2}\times\frac{\pi}{180} = \frac{131\pi}{360}$.

v) $75°30' = 75.5° = \frac{151}{2}\times\frac{\pi}{180} = \frac{151\pi}{360}$.

vi) $40°48' = 40.8° = \frac{204}{5}\times\frac{\pi}{180} = \frac{204\pi}{900} = \frac{17\pi}{75}$ (dividing by $12$).

Multiply the degree measure (converting minutes to a decimal degree first, if needed) by π/180 and simplify.

• Forgetting to convert minutes (') into a decimal fraction of a degree before multiplying by π/180.
• Not simplifying the resulting fraction to lowest terms.
• Dropping the negative sign on a negative degree measure.