Question #07bcc

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Answer 1 · 2017-02-17T18:54:51

Substitute $r cos (θ) for x and r sin (θ) for y$ $rcos(theta)" for "x and rsin(theta)" for "y$ , then write r as a function of $θ$ $theta$ .

Substitute $r cos (θ) for x and r sin (θ) for y$ $rcos(theta)" for "x and rsin(theta)" for "y$ :

$5 r cos (θ) - 4 r sin (θ) = - 7$ $5rcos(theta) - 4rsin(theta) = -7$

Remove the common factor r:

$r (5 cos (θ) - 4 sin (θ)) = - 7$ $r(5cos(theta) - 4sin(theta)) = -7$

Divide both sides by $5 cos (θ) - 4 sin (θ)$ $5cos(theta)-4sin(theta)$ :

$r = \frac{- 7}{5 cos (θ) - 4 sin (θ)}$ $r = (-7)/(5cos(theta) - 4sin(theta))$

Multiply numerator and denominator by -1:

$r = \frac{7}{4 sin (θ) - 5 cos (θ)}$ $r = 7/(4sin(theta)-5cos(theta))$