Thread: getting wrong theta from tan(theta)=-4/3

The exercise asks, convert (-3,4) to polar coordinates.
I get (5, -4.140), but it's wrong. The solution is supposed to be (5, 2.21) or (-5, 5.36).

Why do I keep getting the wrong answer?

Thanks,
Ivy

(-5, 5.36) could not possibly be right, a radius length can only ever be positive...

Anyway, .

Now, notice that (-3, 4) is in the second quadrant, so .

Hello, Ivy!

Sorry, Prove it . . . can be negative.

Convert (-3,4) to polar coordinates.

I get (5, -4.140), but it's wrong.
The solution is supposed to be (5, 2.21) or (-5, 5.36).

Why do I keep getting the wrong answer?
. . How did you get that angle?

Code:

       (-3,4) |
          *   |
          :\  |
         4: \5|
          :  \|
      - - + - + - - - -
            3 |

We see that: .

The angle is: .

This translates to positive angles of: .


You should be aware that there are an infinite number of ways
. . to designate a point in polar coordinates.

Two of the ways are: . and


Recall how polar coordinates are plotted.


The first tells us:
. . stand at the pole (origin), face East, turn 2.21 radians CCW
. . and walk forward 5 units.
This places us at the point in Quadrant 2.

The second tells us:
. . stand at the pole, face East, turn 5.36 radians CCW
. . and walk backward 5 units.
This places us at the same point.

Thank you so much. I get confused about when to use my calculator in radians or degrees mode. Do polar coordinates require that theta always be in rads instead of degrees? When I take the trig. ratio of two sides, will the answer always be in rads?