Question

If u= and v=<3cos45degree,3sin45degree> find the direction of u+v. Put in degrees and round to the nearest tenth.

Answer 1

Answer:

54.0°

Step-by-step explanation:

We have that:

u=<cos 30°, 4sin30°>

This implies that:

u=<½√3, 2>

Also, v=<3cos 45°, 3sin 45°>

v=<3√2/2, 3√2/2>

u+v=<2.99,4.12)

The direction of u+v, is the angle, it makes with the positive x-axis.

This is given by;

$\theta = { \tan}^{ - 1} ( \frac{y}{x} )$

$\theta = { \tan}^{ - 1} ( \frac{4.12}{2.99} )$

$\theta = 54.03$

To the nearest tenth, the direction is 54.0°