ErinWeeks
  • ErinWeeks
Find the magnitude ||v|| and direction angle θ, to the nearest tenth of a degree, for the given vector v.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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ErinWeeks
  • ErinWeeks
@Psymon i need help with 2 more questions..
ErinWeeks
  • ErinWeeks
v = -4i - 3j
Psymon
  • Psymon
Well, theta we can get using a triangle *draws*

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Psymon
  • Psymon
because i refers to the x direction and j refers to the y direction: |dw:1377763945660:dw| Now in order to find theta, we need to use one of our trig functions. Can you look at that triangle and see which trig function would involve using those two sides?
ErinWeeks
  • ErinWeeks
this formula v = ||v|| cos theta i + ||v|| sing theta j ????
Psymon
  • Psymon
Actually, no. Thats more of a form than a formula. So do you understand where I came up with the triangle and the numbers at all?
ErinWeeks
  • ErinWeeks
well i get that -3 is down and -4 is over
Psymon
  • Psymon
Right. i refers to x values and j refers to y values. So the vector -4i - 3j is like saying the end point of my vector is (-4,-3). With that information, I drew the triangle and the side lengths of 4 and 3.
ErinWeeks
  • ErinWeeks
okay i got that
Psymon
  • Psymon
Alright. Now do you know how to use the two sides of a triangle to get an angle?
ErinWeeks
  • ErinWeeks
i dont remember for sure i know you do something then subtract by 180
Psymon
  • Psymon
Well thats if you have other angles. To find the angle we want using the sides of a triangle, we need to use one of the trigonometric functions: \[\sin \theta = \frac{ opposite }{ hypotenuse }\] \[\cos \theta = \frac{ adjacent }{ hypotenuse }\] \[\tan \theta = \frac{ opposite }{ adjacent }\] Kind of ring a bell?
ErinWeeks
  • ErinWeeks
yea it does ring a bell i did this like a year and a half ago
ErinWeeks
  • ErinWeeks
we would be using sin theta right?
Psymon
  • Psymon
Ah, okay. Well, we have to do this using our two sides: |dw:1377764841525:dw| And no, because sin theta uses the hypotenuse. But we dont have a hypotenuse side, only the other two.
ErinWeeks
  • ErinWeeks
my bad lol so were using tan theta than!
Psymon
  • Psymon
Yeah xD So now tan(theta) = what? :P
ErinWeeks
  • ErinWeeks
tan(theta) = 3/4 ?
Psymon
  • Psymon
Yep, absolutely. So that means: \[\tan^{-1} (\frac{ 3 }{ 4 }) = \theta \]
ErinWeeks
  • ErinWeeks
okay dont i solve that ?
ErinWeeks
  • ErinWeeks
if so i got 36.9
ErinWeeks
  • ErinWeeks
thankk you soo much ! Good night .. (:
terenzreignz
  • terenzreignz
NO.
Psymon
  • Psymon
x_x
terenzreignz
  • terenzreignz
What's the magnitude, @ErinWeeks

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