trig functions

[mlane]

If you have a right triangle and you only know 1 distance, how can you solve for the rest of the triangle.

Another Question:
If you take the inverse cosine of a ratio does it give you an angle.

I am not sure of the rules of cosine and sines.

 

[soroban]

Hello, mlane!

If you have a right triangle and you only know 1 distance, how can you solve for the rest of the triangle>

We can't . . . we need one more piece of information.

If you take the inverse cosine of a ratio, does it give you an angle?

Yes, but we must be careful . . . it may not give us the angle.

Suppose we are told that: $\displaystyle \cos\theta\,=\,\frac{1}{2}\,=\,0.5$

Our calculator says: $\displaystyle \theta\:=\:\cos^{-1}(0.5)\:=\:60^o$
. . and it checks out: .$\displaystyle \cos(60^o)\:=\:0.5$

But it is also true that: $\displaystyle \cos(300^o)\,=\,0.5$
. . and $\displaystyle \cos(-60^o)\,=\,0.5$ . . . and $\displaystyle \cos(420^o)\,=\,0.5$

Which of these is the correct answer? .It depends on the nature of the problem.