How do you find the component form of v given its magnitude 1 and the angle it makes with the positive x-axis is #theta=45^circ#?

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Answer 1 · 2018-01-16T13:31:43

See below.

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There are various ways we can solve this, so this is just one of them.

Let #v# have components #x# and #y#, such that:

#v=((x),(y))#

#||v||=sqrt((x)^2+(y)^2)=1#

#:.#

#x^2+y^2=1#

This is the equation of a circle, with radius 1 and centre at the origin.

For any point on the circumference of this circle, the coordinates #( x ,y)# can be represented by:

#(rcos(theta),rsin(theta))#

Since our vector makes an angle of #45^@# with the x axis, we have:

#(rcos(45), rsin(45))#

Our radius is equal to the magnitude of #v# and #v=1#, so:

#(sqrt(2)/2,sqrt(2)/2)# #v=((sqrt(2)/2),(sqrt(2)/2))#

or #sqrt(2)/2hati+sqrt(2)/2hatj#