We're asked to determine the **y****-component** and **magnitude** of a vector given its direction and *x*-component.

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

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

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

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

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

Vector **A** is in the direction 34.0° clockwise from the −y-axis. The x-component of **A** is A_{x} = −16.0 m.

(a) What is the y-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 Jerousek's class at UCF.