Change from one vector form to another

[1irishman]

Homework Statement

Change to polar form: F = {5.0i - 2.0j} N

Homework Equations

a^2 + b^2 = c^2

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.
Help please? Thanks.

 

[librab103]

Homework Statement

Change to polar form: F = {5.0i - 2.0j} N

Homework Equations

a^2 + b^2 = c^2

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.
Help please? Thanks.

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

 

[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?

 

[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.

 

[1irishman]

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

 

[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
cosine = adjacent/hypotenuse
tangent = opposite/adjacent

 

[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.

 

[1irishman]

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