Consider a nondegenerated right triangle with sides of length $\sin x$, $\cos x$, and $\tan x$ where $x$ is a real number. Compute the possible values of the area of this triangle.
- I was thinking of more along the lines of Heron's formula but that was very nasty indeed, rather I have attempted to find out what are the lengths of the triangle and I have done the Pythagorean theorem which was in vain.
Another thing that I have done was to graph all three and to see which one was the largest in the y-value but it turned out that at times one graph was larger than the other and at other times it wasn't.
And another thing that I have done was to plug and chug in values such as the number 3 into all of the trig functions and do Pythagorean theorem to see if it satisfied it but none of them didn't
The reason why that I have done those steps was so that I can multiply the legs and divide by two to find the area of the triangle but in order to do that I must know what are the legs.
I was wondering if there was any other way?