Question

Find the magnitude ||v|| and direction angle θ, to the nearest tenth of a degree, for the given vector v.

Answer 1

@Psymon i need help with 2 more questions..

Answer 2

v = -4i - 3j

Answer 3

Well, theta we can get using a triangle *draws*

Answer 4

because i refers to the x direction and j refers to the y direction:



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?

Answer 5

this formula v = ||v|| cos theta i + ||v|| sing theta j ????

Answer 6

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?

Answer 7

well i get that -3 is down and -4 is over

Answer 8

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.

Answer 9

okay i got that

Answer 10

Alright. Now do you know how to use the two sides of a triangle to get an angle?

Answer 11

i dont remember for sure i know you do something then subtract by 180

Answer 12

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?

Answer 13

yea it does ring a bell i did this like a year and a half ago

Answer 14

we would be using sin theta right?

Answer 15

Ah, okay. Well, we have to do this using our two sides:



And no, because sin theta uses the hypotenuse. But we dont have a hypotenuse side, only the other two.