Question

Consider the vector v=(5,8). What is the angle between v=(5,8) and the positive x-axis?

Answer 1

you can consider x- axis is a vector u = (1,0) and find the angle between them by formula theta = ..... do you know that formula?

Answer 2

Nope, all i know is the quesstion. I just learned this tsuff

Answer 3

\[\theta = \cos^-(\frac{ u.v}{ ||u||||v||})\]

Answer 4

that' it

Answer 5

You would bput the numbers in with the equation but which number goes in which spot?

Answer 6

oh, those are not numbers, those are vectors, and from numerator, vector u dot vector v. in denominator, ||u|| is the length of vector u and ||v|| is the length of vector v. you have formulas to figure out all of them

Answer 7

So ino order to do this you will have to find the distance of V withc would be 5^2+*^2 right?

Answer 8

\[||v||= \sqrt{5^2 +8^2}\]. you forgot sqrt

Answer 9

length will be \[\sqrt{89}\]

Answer 10

yes

Answer 11

Then length of u =1

Answer 12

yes

Answer 13

Ok so how would we distribute for equation?

Answer 14

how about u dot v at numerator?

Answer 15

\[\frac{ \sqrt{89}\times1 }{ \left| 1 \right| }\left| \sqrt{89} \right|\]

Answer 16

Not sure on bottom

Answer 17

nope, u dot v = < (1,0), (5,8)> = 1*5 + 0*8 = 5 . that's just numerator, your denominator is sqr (89)
so combine them you get \[\theta = \cos^- \frac{ 5 }{ \sqrt{89} }\]

Answer 18

you have to use calculator to find the theta if you want answer in number, if not, that 's your answer, it's ok, too.

Answer 19

For the exact number I got 57.99461679

Answer 20

I don't do that part, trust yourself from that part.

Answer 21

Alright, Thank you for your help!

Answer 22

np