Find the component form of v.

Question

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

 

Magnitude: 9/7

Angle: θ=150°

Answer 1

Make a little drawing of an angle in standard position, measuring 150 degrees.  Beneath the vector is its 30 degree REFERENCE angle.  Look at the right triangle that has its horizontal leg on the x-axis (from the origin to the left. Look at the vertical leg of this reference triangle.

 

The vertical leg is (9/7) sin 150^o = (9/7)(1/2) = 9/14.

The horizontal leg is (9/7) cos 150^o = (9/7)(-√(3)/2) ... negative because it's in the second quadrant.

 

These are the components of vector v: ( -9√(3)/2, 9/14)   <------ corrected (were put in wrong order!!) ks