Find the magnitude and direction angle of v=7(cos140i+sin140j. Show your work?

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Answer 1 · 2018-04-06T21:28:05

Magnitude = 7
thetha = -40 degrees, since the x component it negative it will be 40 degrees north of west

#v= 7(cos(140)i+sin(140)j)# (Use a calculator to find the sine and cosine of 140)

#v= 7(-0.766i+0.643j)# (Distribute 7 to the numbers in brackets)

#v=-5.36i+4.50j# (This is the component form)

To find the magnitude, use the Pythagorean theorem

#v^2=(-5.36)^2+(4.50^2)#

#v^2=28.7+20.3# (Combine numbers)

#v^2=49# (square root to get magnitude)

#sqrt(v^2)=sqrt49#

||v||=7

To find the direction, use inverse tan on the component form

#thetha=tan^-1(4.50/-5.36)#

thetha = -40 degrees, since the x component it negative it will be 40 degrees north of west