Question

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Round to the nearest thousandth.

||v|| = 3/4 * = 30 degrees

* is theta
photo for reference

Answer 1

0.650i + 0.375j

Or,

< 0.650 , 0.375 >

Explanation:

In the i-direction is the horizontal component:

x = ||v|| cos(theta)

x = ¾ cos(30)

x = 0.6495190528

In the j-direction is the vertical component:

y = ||v|| sin(theta)

y = ¾ sin(30)

y = 0.375

Answer 2

see below

Explanation:

||v|| = 3/4

Theta = 30 degrees

The x component is x = ||v|| cos theta

= 3/4 cos 30 =3/4 * sqrt(3) /2 =3 /8 sqrt(3) =.649519053= .650

The y component is y = ||v|| sin theta

= 3/4 sin 30 =.375