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

Question

19054 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-16T13:31:43

See below.

enter image source here

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 $sqrt(2)/2hati+sqrt(2)/2hatj$

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^circtheta=45^circ?