Specifically something like sinx=-4 and cosx=-1
I think your question is misleading. To find the "sine of a number" you would use a calculator. But from your examples, it seems you want to solve for x, when x is in a trig function.
Simply take the inverse of the trig function.
The inverse functions are symbolized by the inverse sign, e.g., .
Also, if you are not allowed to use a calculator, the you can use a "unit circle" for common angles.
I've read that you can use triangles to solve for inverse functions, but I can't wrap my head around it. I understand how to get
using a special right triangle, but how can you get sinx=-4 using that technique?
Are you using only real numbers or can you use imaginary numbers for this problem?
If you are using only real numbers, then sinx = -4 has no real solution, since -1 <= sinx <= 1. So the answer would be "No Solution."
As for the other example you gave, cosx = -1, that is in the domain of cos, so we can get x = pi.
Two methods come to mind. My favorite: use a calculator. TI-84 Plus is my personal pick.
Of course, you can do this one by using the unit circle also. is in radians. In degrees, that same angle is 90 degrees. If on a xy plane you draw a line that is at 90 degrees, you are drawing a line straight up. One unit up is at the point (0,1), right? Since cos(t) = x, then we just look at the x value, which is zero. So...
I was always told to memorize the unit circle. And I never, ever did. I was able to get by though by using my calculator and by creating the unit circle using simple logic whenever I really needed it. I still don't have most of the basic angles memorized, I always check with my calculator.
That being said, my advice is to memorize the common angles, as it will really help out in the years to come. I still waste time creating the unit circle when if I just had it memorized it would save me a minute or two.