For any problems that ask us to relate the magnitude, angle, and components of a vector, there are **two fundamental equations** we'll use:

$\overline{)\left|\stackrel{\mathbf{\rightharpoonup}}{\mathbf{A}}\right|{=}\sqrt{{{A}_{x}}^{2}+{{A}_{y}}^{2}}}$ (1)

$\overline{){\mathrm{tan}}{\theta}{=}\frac{{A}_{y}}{{A}_{x}}}$ (2)

where *θ* is the angle of the vector measured **counterclockwise from the + x-axis**. (By convention, counterclockwise is the positive direction for angles.)

__It's also a good idea to sketch the problem so you can more easily visualize it.__

**(a)** For this part of the problem, we're asked to determine the *x*-component of the vector, *A _{x}*. We're given the vector's

Since the given angle isn't measured from the +*x*-axis, __we'll need to determine what our θ is__. It's in Quadrant 2, which means that if we want it as a positive angle,

$\theta =90\xb0+32\xb0=122\xb0$

Vector **A** has y-component *A*_{y}* *= +15.0 m and makes an angle of 32.0° counterclockwise from the +*y*-axis.

**(a)** What is the *x*-component of **A**?**(b)** What is the magnitude of **A**?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Trig Review concept. You can view video lessons to learn Trig Review. Or if you need more Trig Review practice, you can also practice Trig Review practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Vuki's class at University of Guam.