Find the magnitude and the direction sum A+B?

Question

A= 10 ; direction =30, clockwise from the positive x axis

B=20; direction=60, clockwise from the positive y axis

I am not sure how to picture this. Also I know I am supposed to find the X and Y for both of them. I am not sure when to use sin or cos.

Please explain

Answer 1

how to picture this? Draw a set of XY axis, draw vectors (lines with  an arrow on the end) at the angles and lengths listed.

I'll use the positive X axis as 0 degrees, positive angles CCW from there, which is the standard for angles and vectors.

A = 10 angle -30

B = 20 angle +30

When to use cos and sin? review your definitions of sine and cos, and tan. But easy to remember, use cos for x component, sin for y component, and arc tan to convert from components to angle.

Ax = 10 cos (-30) = 8.66

Ay = 10 sin (-30) = -5.00

Bx = 20 cos (30) = 17.32

By = 20 sin (30) = 10.00

Cx = 25.98

Cy = 5.00

C magn = √(25.98² +5²) = 26.46

C angle = arc tan (5/25.98) = 10.89 degrees