Resolved: "Convert each polar equation to rectangular form. =−π6"

High School
Calculus and Analysis
Calculus 2
Parametric equations

Armorikam

Answered question

2021-09-08

Convert each polar equation to rectangular form. $= - \frac{π}{6}$

Answer & Explanation

Sadie Eaton

Skilled2021-09-09Added 104 answers

1) $θ = - \frac{π}{6}$
$\tan θ = \tan (- \frac{π}{6})$
2) $\tan θ = \frac{\sin θ}{\cos θ}$
$\frac{\sin θ}{\cos θ} = - \frac{\sqrt{3}}{3}$
3) Replace $\sin θ$ with $y$ and $\cos θ$ with $x$
$\frac{y}{x} = - \frac{\sqrt{3}}{3}$
4) Multiply both sides by $x$
$y = - \frac{\sqrt{3}}{3} \times x$
$y = - \frac{\sqrt{3}}{3} \times x + 0$
This is the equation of a line with slope of $- \frac{\sqrt{3}}{3}$ and y-intercept of 0.

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