# Homework Help: Change from one vector form to another

1. Sep 29, 2009

### 1irishman

1. The problem statement, all variables and given/known data
Change to polar form: F = {5.0i - 2.0j} N

2. Relevant equations
a^2 + b^2 = c^2

3. The attempt at a solution
The answer is F = 5.4N at 21.8 degrees South of East
I understand how they got 5.4N, but I don't understand how they got 21.8 degrees.

2. Sep 29, 2009

### librab103

You need to remember which axis i and j relate too. Also pay attention to the sign for j.

3. Sep 29, 2009

### 1irishman

Yeah i is x axis and j is y axis and j in this case is negative and i is positive, but i still don't know how they got the angle of 21.8 degrees. Can someone help please?

4. Sep 29, 2009

### Delphi51

Make a sketch! Draw a line 5 to the right and then a line 2 down. The vector (5i,-2j) goes from where you started to where you ended. You have a right triangle. You could measure the angle with a protractor if you have drawn the triangle accurately. Or calculate it using trigonometry. If you take the standard map directions of East to the right and south downward, you'll see the vector points southeast. From the eastward horizontal line, the vector is 21.8 degrees off horizontal toward the south, commonly described as South of East.

5. Sep 29, 2009

### 1irishman

I want to calculate it using trig...but i don't know what function to use...sin, cos, or tan?

6. Sep 29, 2009

### Delphi51

Name the sides that are 2 and 5, relative to the angle.
The "adjacent" side is next to the angle. The "opposite" side is way over on the side furthest away from the angle. The "hypotenuse" is the side opposite the right angle.
Pick the trig function that includes the two sides you know (2 and 5):
Sine = opposite/hypotenuse

7. Sep 29, 2009

### 1irishman

Okay, i think i'm getting closer because i am using tan function...so that would look like tan=2/5 and then i would get answer? Sorry, i am not to good at this.

8. Sep 29, 2009

### 1irishman

Okay, i got it now thanks...awesome help! :-)