How do you convert $(- 4, \frac{π}{6})$ $(-4,pi/6)$ to rectangular form?

Question

How do you convert $(- 4, \frac{π}{6})$ $(-4,pi/6)$ to rectangular form?

1 Answer

Impact of this question

2312 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-06T03:42:40

$(x, y) \Rightarrow (- 2 \sqrt{3}, - 2)$ $(x,y) => (-2sqrt3,-2)$

Explanation:

$(r, θ) \Rightarrow (- 4, \frac{π}{6})$ $(r,theta) => (-4,pi/6)$

$\frac{π}{6} = 30$ $pi/6=30$ degrees

This means we are working with the special triangle 30-60-90

30 degrees corresponds to $1$ $1$ => OPPOSITE SIDE
60 degrees corresponds to $\sqrt{3}$ $sqrt3$ => ADJACENT SIDE
90 degrees corresponds to $2$ $2$ => HYPOTENUS

cosine $\Rightarrow \frac{a d j}{h y p}$ $=> (a d j) / (h y p)$
sine $\Rightarrow \frac{o p p}{h y p}$ $=> (o p p) / (h y p)$

Make the necessary substitutions

$x = r cos (θ) = - 4 cos (\frac{π}{6}) = - 4 (\frac{\sqrt{3}}{2}) = - 2 \sqrt{3}$ $x=rcos(theta)=-4cos(pi/6)=-4(sqrt3/2)=-2sqrt3$
$y = r sin (θ) = - 4 sin (\frac{π}{6}) = - 4 (\frac{1}{2}) = - 2$ $y=rsin(theta)=-4sin(pi/6)=-4(1/2)=-2$

$(x, y) \Rightarrow (- 2 \sqrt{3}, - 2)$ $(x,y) => (-2sqrt3,-2)$

Click on the video tutorials below for more information

Science

Math

Humanities

... and beyond

How do you convert $(- 4, \frac{π}{6})$ $(-4,pi/6)$ to rectangular form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you convert (−4,π6)(-4,pi/6) to rectangular form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you convert $(- 4, \frac{π}{6})$ $(-4,pi/6)$ to rectangular form?