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प्रश्न
Convert the following angles into radian:
40°48′
उत्तर
We know that, 180° = πc
∴ 1° = `(pi/180)^"c"`
∴ 40°48′ = 40° + 48'
= `40^circ + (48/60)^circ ...[∵ 1^circ = 60 "'" "so", 1"'" = (1/60)^circ]`
= `40^circ + (4/5)^circ`
= `(40 + 4/5)^circ`
= `((5 xx 40 + 4)/5)^circ`
= `((200 + 4)/5)^circ`
= `(204/5)^circ`
= `(204/5 xx pi/180)^"c"`
= `(cancel(204)^102/5 xx pi/cancel(180)_90)^"c"`
`= (cancel(102)^51/5 xx pi/cancel(90)_45)^c`
`= (51/5 xx pi/45)^c`
`= (51 pi)/225`
`= (17pi)/75`
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