Question

If a vector A⃗ has the following components, use trigonometry to find its magnitude and the counterclockwise angle it makes with the +x axis: Ax = 9.00lb , Ay = 5.00lb

Answer 1

what is lb? pounds?

Answer 2

Magnitude is\[\sqrt{A_{x}^2 + A_{y}^2}\]


Angle \[\tan \theta = A_{y}/A_{x} \]

therefore \[\theta = \tan^{-1}(A_{y}/A_{x}) \]

Answer 3

i plugged in the numbers for the last equation and it said the answer was wrong

Answer 4

is your calculator in radians or degrees?

Answer 5

in degreees

Answer 6

29 degrees is incorrect?

Answer 7

i found a different number but 29 was correct can you explain how you found that?

Answer 8

\[\tan ^{-1}({\frac {A_y} {A_x}})= \tan ^{-1}({\frac {5} {9}})\]

Answer 9

did your calculator give you 0.507?

Answer 10

no this time i got 29 i must have entered it wrong the first time

Answer 11

cool then

Answer 12

thank you! if you have time one more thing, same type of problem but its with
Ax = -24.0m/s , Ay = -34.0m/s

i got 54.78 but it is supposedly the wrong answer

Answer 13

ah, negatives are tricky

Answer 14

yeah i just tried solving it the same and it wasn't working out i guess

Answer 15

234.8

Answer 16

thats correct, how did you get that

Answer 17

your calculator gave you 54.8 right?

Answer 18

right

Answer 19

54.8 is also correct

Answer 20

divide Ay/Ax and tell me what you get
then take tangent of BOTH angles you got

Answer 21

you'll notice there's no difference

Answer 22

well i did -34/-24 and then i took the \[\tan^{-1} \] 1.41667 and got 54.78 what would the other angle be?

Answer 23

oops, sorry, i meant
tan(54.78)
tan(234.78)
don't do \[tan^{-1}\]

Answer 24

ok yeah i get the same angles. but how did you get the 234.78?

Answer 25

you have to do that yourself. see, while a calculator is good at performing hard calculations, it's not very smart. so what it does is, it goes around the 4 quadrants starting from quadrant 1 until it finds an angle that will give you 1.41667. So it never reaches 278 because 54.78 already gives you that number, does that make sense?

Answer 26

so for example, sin(30)=sin(150)=1/2
but if you do sin ^-1 (1/2) you will NEVER get 150, you will always get 30. does that make sense?

Answer 27

yes that makes sense. so how do i do it myself?

Answer 28

ok, that really depends on the trig function you're talking about.
for tangent, just add 180
but for sin, it has to be 180- the angle.

Answer 29

so 180-30=150

Answer 30

54.78+180=278.78

Answer 31

but just to check, you can always just do the reverse after adding or subtracting.
there is a derivation to all of this

Answer 32

ok that makes total sense thank you! this has been very helpful

Answer 33

hey no problem

Answer 34

and remember

Answer 35

calculators are stupid

Answer 36

=D

Answer 37

sorry, just had to say that

Answer 38

haha no problem they cause me more harm then good most of the time