Using the Distributive Property
The answer would be 3.
2 *4x = 8x and 2 * 3 = 6, to get 8x 6
is in quadrant I, so
.
is in quadrant II, so
.
Recall that for any angle
,

Then with the conditions determined above, we get

and

Now recall the compound angle formulas:




as well as the definition of tangent:

Then
1. 
2. 
3. 
4. 
5. 
6. 
7. A bit more work required here. Recall the half-angle identities:



Because
is in quadrant II, we know that
is in quadrant I. Specifically, we know
, so
. In this quadrant, we have
, so

8. 
F1 = 6*cos(30) i + 6*sin(30) j = 5.20 i + 3 j
<span>F2 = 0 i + 5 j </span>
<span>R = F1 + F2 </span>
<span>Add the 'i's together (x direction) and the 'j's together (y direction) </span>
<span>R = (5.20 + 0) i + (3 + 5) j = 5.2 i + 8 j </span>
<span>Magnitude: </span>
<span>||R|| = </span>√<span>(5.2^2 + 8 ^2) = </span>√<span>91 = 9.54 </span>
<span>Direction: </span>
Θ<span> = atan ( Rj / Ri ) = atan( 8 / 5.2 ) = 57.0</span>⁰