if `rsintheta=(7)/(2) and rcostheta=(7sqrt(3))/(2),` then value of r is

Options

A. 4
B. 3
C. 5
D. 7

Answer

d

Explanation

`r sin theta=(7)/(2)` .......(i)
`r cos theta=(7sqrt(3))/(2)` .......(ii)
On squaring and adding both equations
`r^(2)sin^(2)theta+r^(2)cos^(2)theta=((7)/(2))^(2)+((7sqrt(3))/(2))^(2)`
`r^(2)(sin^(2)theta+cos^(2)theta)=(49)/(4)+(147)/(4)`
`r^(2)=(196)/(4)=49`
`r=sqrt(49)=7`