Find the magnitude and direction angle for each vector. Give the measure of the direction angles as an angle in [0, 360 degree]

Question

Find the magnitude and direction angle for each vector. Give the measure of the direction angles as an angle in [0, 360 degree]
<-12, 5>

johnweldon1993 · Answer

$$\large |v| = \sqrt{-12^2 + 5^5}$$

$$\large \theta = \tan^{-1} (\frac{5}{-12})$$

anonymous · Answer

i got it...but tan theta is negative...and i dont know how to get the reference theta for this problem

johnweldon1993 · Answer

Just add it to 180...

So $$\large \tan^{-1}(\frac{5}{-12}) = -22.61986$$

So $$\large 180 - 22.61986 = 157.38^\circ$$

anonymous · Answer

hold on...so we got tan is negative...so theta have to be in Quadrant II or IV
so how if i get theta = 360 +( - 22.61986) ?

johnweldon1993 · Answer

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anonymous · Answer

oh ok...yeah...reference agle...i know that
theta at Q I = theta
theta at Q II = 180- theta
theta at Q III = 180 + theta
theta at Q IV = 360 - theta
but whats the different between positive and negative theta?

johnweldon1993 · Answer

Well when we are in quadrant I  ...we have a positive theta
Quadrant III we have negative/negative so again a positive theta...

The only difference is...since we generally move counterclockwise when reading...we leave the Q I theta as it is...since it is just the angle to the horizontal axis that we want

In Q III we also have a positive theta...but we are adding onto the 180 degrees from the horizontal axis that we wanted

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johnweldon1993 · Answer

If we were in the 4th quadrant...

see how it says...subtract theta from 360 ??

That is because we want

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