Find the least and greatest values of the distance of the point `(costheta,sintheta),theta in R ,` from the line `3x-4y+10=0.`

Explanation

Distance of point `("cos" theta, "sin" theta)` from the line 3x-4y+10=0 is
`d = (|3"cos" theta - 4 "sin" theta +10|)/sqrt(3^(3)+(-4)^(2))= (|3"cos" theta-4"sin" theta+ 10 |)/(5)`
`"Now", -5 le 3"cos" theta - 4"sin" theta le 5`
`5 le 3"cos" theta - 4"sin" theta +10 le 15`
`rArr 1 le (| 3"cos" theta - 4"sin" theta +10|)/(5) le 3`
Hence, the least distance is 1 and the greatest distance is 3.