Convert the following from rectangular to polar and vice versa?

Question

All answers must by in positive radians
a) (3,-4) - to polar
b) (-13,12) - to polar
c) (5, (3(pi))/2 ) - to rectangular
d) (12,.75) - to retangular

Answer 1

5, 5.3559
17.6918, 2.3962
0, -5
8.7803, 8.1797

Done with the Pol and Rec buttons on the calculator, hopefully correctly. For more exact answers (z is theta):

Q1

x=3, y=-4
r=(x^2 + y^2)^0.5
r=(3^2 + (-4)^2)^0.5 = 5
z=tan^-1(y/z)
z=tan^-1(-4/3) ~= -0.9280
It's in the right quadrant
Now add 2pi to get a positive number - 5.3559

Apply the same to the next question.

Now, question 3:
sin (z) = x/5
sin (3pi/2) = y/5
y = -5
cos (z) = y/5
cos (3pi/2) = x/5
x = 0

Same method for q 4.

Hmm, sounds like homework - if it is then - do your homework yourself in future ;)

Answer 2

(a)Use the Pythagoras Theorem (a^2+b^2=c^2).Then take the sqrt of the result.Then use the formula tan (angle)=y/x.Then take the inverse tangent of the angle.U should get the result (5,-53.1 degrees).Use the smae method 4 (b).(c)In this case there are two formulas.They are (x=r cos (angle)) and (y=r sin (angle)).Use the first formula first.In this case x=(5 cos(3(pi))/2).Which is approximately 23.56 degrees.This result will be the x-coordinate.Then use the second formula.In this case y=5 sin (3(pi))/2) which is approximately 0.41.This will be the y-coordinate.There4 the answer is (23.56,0.41).Use the same method for (d).

Answer 3

(a) 5 ∟- 53.13º..... ( ∟ means the angle of ......)

(b) 17.691... ∟ 137.29º.....

(c) 3π /2 = 270º
5 ∟270º = (0 - j 5)

(d) (12, 0∙75) - it looks like (point) 0∙75.
= 11.998... + j 0∙157
If that should be 75 and not 0∙75 then the answer is:
= 3.105... + j 11∙591...

Answer 4

certainly, i've got faith like the two considered one of those persons did it incorrect.. tan=sin(theta)/cos(theta) sin(pi/3)--> sqrt(3)/2 cos(pi/3)--> a million/2 So, (sqrt(3)/2)/(a million/2)= sq. root of three. this equals y/x So, sqrt(3)=(y/x) y=(sq. root 3)x

Answer 5

Read the textbook and do your own homework. Show where you are stuck and then you can have help.