# Question 390b7

Aug 30, 2017

Use your old friend, Mr. Pythagoras...

#### Explanation:

Calculate the magnitude (length) of the vector using the formula:

$r = \sqrt{{x}^{2} + {y}^{2}}$

...where x & y are the respective components of the vector.

I'll do (a) for you, which should be enough to get you started.

r = sqrt(1.95^2 + (-0.70)^2#

= 2.0718... (I rounded off).

...now remember that $\frac{x}{r} = \cos \left(\theta\right)$
...and $\frac{y}{r} = \sin \left(\theta\right)$

$\sin \left(\theta\right) = - \frac{.7}{2.0718} = - 0.3379 \ldots$
$\theta = - 19.746 \ldots \left(\mathrm{de} g r e e s\right)$

similarly, calculating $\theta = \arccos \left(\frac{1.95}{2.0718}\right)$ gives 19.746 degrees.

Since the cosine of the angle is positive, and the sine of the angle is negative, you can deduce that the angle is in the 4th quadrant (which matches what you know since your x component of the original vector is positive, and the y component is negative).

Note, though, that the problem states that the angle is to be given measured counterclockwise from the x axis. -19.746 degrees measures it CLOCKWISE from the x axis. To convert this to the required answer, subtract 19.746 from 360...giving

340.253... degrees. (rounding off).

GOOD LUCK!