Question

How do I know when to use sine, cosine, or tangent when solving a vector?

Answer 1

Answer:

It depends on what values you know and what is your unknown.

Explanation:

When you investigate the components of a vector, you normally use component in two axes which are perpendicular to each other, and decompose the vector in component in such axes.

The fact that the components are perpendicular is quite important, because you can use trigonometric functions associated with a right angle triangle (see attached figure).

Once you have clear which of the two acute angles is going to be used to define the trigonometric relationships, you can immediately assign the following names to the vector components and to the vector itself. Please look at the picture.

The component "opposite" to the angle you will be using is referred to as "opp" in the image (this is pictured in blue). The component "adjacent" to the angle of reference is called "adj" in the image and pictured in green,

The actual vector is the "hypotenuse" of the right angle triangle defined by the vector and its components and referred as "hyp" in the picture (pictured in red in the image).

Now, depending on what component you need to find, you use the most convenient trig relationship (the one that has more known values) to find an unknown. These relationships are:

$sin(\theta) = \frac{opp}{hyp} \\cos(\theta) = \frac{adj}{hyp} \\tan(\theta)= \frac{opp}{adj}$

and solve in the selected simple ratio for the unknown.