Vector magnitude and direction

• Mar 31st 2009, 01:18 PM
strgrl
Vector magnitude and direction
A vector has an x component of -25.0 units and a y component of 40.0 units. Find the magnitude and direction of this vector.

I found magnitude to be 47.2 units (using Pythagorean theorem) but am unsure how to solve for direction. Could someone please help?

Thank you.
• Mar 31st 2009, 01:52 PM
Plato
The angle the vector makes with the positive x-axis is $\pi - \arctan \left( {\frac{8}{5}} \right)$.
• Mar 31st 2009, 02:49 PM
strgrl
I'm sorry, but I'm not sure how you got that answer. I was trying to determine angle based on sin(t) = opp/hyp giving sin(t)=0.847. t= 58. However, the books lists the answers as 122 degrees. I do know how to fix this discrepancy.
• Mar 31st 2009, 02:54 PM
TheEmptySet
Quote:

Originally Posted by strgrl
I'm sorry, but I'm not sure how you got that answer. I was trying to determine angle based on sin(t) = opp/hyp giving sin(t)=0.847. t= 58. However, the books lists the answers as 122 degrees. I do know how to fix this discrepancy.

You have the answer partially correct...

From the info in the start of the problem you know the vector is in the 2nd quadrant. (x is negative and y is posative)

So the angle you got is the reference angle in the 2nd quadrant (it is the measure of the angle from the negative x axis not the posative)

so the measure of the angle is $180^\circ - 58^\circ=122^\circ$

Draw a picture and you will see what I mean.

Good luck
• Mar 31st 2009, 03:11 PM
Plato
Quote:

Originally Posted by strgrl
I'm sorry, but I'm not sure how you got that answer. I was trying to determine angle based on sin(t) = opp/hyp giving sin(t)=0.847. t= 58. However, the books lists the answers as 122 degrees. I do know how to fix this discrepancy.

"the books lists the answers as 122 degrees"
This must be a science textbook.
Most mathematicians do not care for degrees. We like numbers.
• Mar 31st 2009, 03:21 PM
TheEmptySet
Quote:

Originally Posted by Plato
"the books lists the answers as 122 degrees"
This must be a science textbook.
Most mathematicians do not care for degrees. We like numbers.

Here here