Write in Terms of sine and cosine and simplify

I am having problems understanding how to solve this equation, or what it is asking, any clarification would be much apprreciated!

Write the trigonometric expression in terms of sine and cosine, and then simplify.

$cos$$(t)$ $tan$$(t)$

1 Answer

Although this might be a little bit vague I still think it might help you understand.

Your example is not really a equation. It is a mathematical expression. For example $$ x, x^2, \frac{15}{3}\cdot\frac{1}{x}, \sin{x}, \cos{x}, \ldots $$ are mathematical expressions. Equation is intuitive way means putting two (or more) mathematical expressions into equality (and you can discuss whether the equality is true or not). Numbers are mathematical expressions e.g. 1,2. We can write equation $$ 1 = 2 $$ In this case it is obviously not true.

Hint

Back to your problem. We have mathematical expression $$ \cos{(t)}\tan{(t)} $$ The task is to rewrite the expression using only $\sin$ and $\cos$. Since $\cos{(t)}$ is already one of the expressions we don't have to do anything with it, but $\tan{(t)}$ is not. But, how is the $\tan$ function defined? It is $$ \tan{(t)}\stackrel{def.}{=}\frac{\sin{(t)}}{\cos{(t)}} $$ So now, whenever we see $\tan{(t)}$ we can write $\frac{\sin{(t)}}{\cos{(t)}}$ instead. Try to apply it to your problem.

Note

I am not sure, where I should have used expression and where term. So if anyone wants to correct that I'd be glad if he/she does so.