+0

+1
145
2

9.) Transform each polar equation to an equation in rectangular coordinates and identify its shape:\

r = (4 / (2cosθ - 3sinθ));

10.) compute the modulus and argument of each complex number.

a.) -5

b. )-5 + 5i

May 28, 2019

#1
+3

9.)

$$r\ =\ \frac{4}{2\cos\theta-3\sin\theta}\\~\\ r(2\cos\theta-3\sin\theta)\ =\ 4\\~\\ 2r\cos\theta-3r\sin\theta\ =\ 4\\~\\ 2x-3y\ =\ 4\qquad\ \qquad\ \qquad\text{because}\qquad x=r\cos\theta\qquad\text{and}\qquad y=r\sin\theta\\~\\ 2x\ =\ 4+3y\\~\\ 2x-4\ =\ 3y\\~\\ \frac23x-\frac43\ =\ y\\~\\ y\ =\ \frac23x-\frac43$$

This is the equation of a line with a slope of   $$\frac23$$   and a y-intercept of  $$-\frac43$$ .

(You can show or hide the second equation by clicking the gray circle to the left of it. )

May 28, 2019

#1
+3

9.)

$$r\ =\ \frac{4}{2\cos\theta-3\sin\theta}\\~\\ r(2\cos\theta-3\sin\theta)\ =\ 4\\~\\ 2r\cos\theta-3r\sin\theta\ =\ 4\\~\\ 2x-3y\ =\ 4\qquad\ \qquad\ \qquad\text{because}\qquad x=r\cos\theta\qquad\text{and}\qquad y=r\sin\theta\\~\\ 2x\ =\ 4+3y\\~\\ 2x-4\ =\ 3y\\~\\ \frac23x-\frac43\ =\ y\\~\\ y\ =\ \frac23x-\frac43$$

This is the equation of a line with a slope of   $$\frac23$$   and a y-intercept of  $$-\frac43$$ .

(You can show or hide the second equation by clicking the gray circle to the left of it. )

hectictar May 28, 2019
#2
+1

10.) compute the modulus and argument of each complex number.

a.)   -5

We have the form      -5 + 0i

The modulus is   √ [ (-50^2 + 0^2 ]  =  √25  = 5

The argument is θ  so   tan θ  =   0 / -5  =  pi

b. )  -5 + 5i

Modulus  =  √[ (-5)^2 + (5)^2 ]  = √ [ 50]  = 5√2

The argument is θ  so   tan θ  =  5/-5  = - 1  =  3pi/4   May 29, 2019