Expert: Paul Klarreich - 2/25/2009

Question
Express the number in polar form. (Give your angle measure as a value θ(greater than of equal to < ) θ < 2π.)

-sqrt(6)-2i

I got the r value of sqrt(10)
but i'm having trouble finding the angles.. any help?

i did:
sinθ= (-2)/sqrt(10)




OTHER PROBLEMS RELATED: all the same issue...

1. 6-2i
got an r value of 6.325
can't figure out the angles.

2. (6-6i)(2-2i)
i got 24 as the r value, still angles I can't get. I don't know the rules for quadrants and how you know how to get the angle in the right quad.  

Answer
Questioner:   ray
Category:  Calculus
Private:  No
 
Subject:  polar form
Question:  Express the number in polar form. (Give your angle measure as a value θ (greater than of equal to < ) θ < 2π.)


>> I think you mean:  0 <= t <= 2 pi

>> These special symbols just get messed up.  I use t for theta.
................................

-sqrt(6)-2i

I got the r value of sqrt(10)

>> OK, so far.

but i'm having trouble finding the angles.. any help?

i did:
sinθ= (-2)/sqrt(10)

Now you really (I mean really) have to know your trig, especially about quadrants.

You have  x = - sqrt(6),  y = -2.  
You are in quadrant 3, because x and y are both negative.  (If x,y both neg, where do you think it is?)

sin t= (-2)/sqrt(10)

>> Ok, now use your calculator.

sin t = -0.63245553203367586639977870888654

t = -39 degrees (approx)

But that is in Quad 4.  So fix it:  Find an angle in quad 3 with the same 39-degree reference angle.  In this case, it's  180 + 39 = 219.

Go back to your trig book and do all those reference angle exercises over again, and again, and again,....
.......................................

OTHER PROBLEMS RELATED: all the same issue...

1. 6-2i
got an r value of 6.325
can't figure out the angles.


>> Same stuff.  Now  x = 6 (++), and  y = -2 (neg)  Which quadrant contains this point?  


2. (6-6i)(2-2i)

>> Multiply it out.  =  0 - 24i.

Where is the point  (0,-24) located?  Draw it and see. No substitute for making a REALLY GOOD, NEAT, PRECISE PICTURE.

i got 24 as the r value, still angles I can't get. I don't know the rules for quadrants and how you know how to get the angle in the right quad.