# Thread: How do you find the sin, cos, or tan of a number?

1. ## How do you find the sin, cos, or tan of a number?

Specifically something like sinx=-4 and cosx=-1

2. 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.

$
\cos{x} = \frac{1}{2}
$

$x = \arccos{\frac{1}{2}}$
$x = \frac{\pi}{3}$

The inverse functions are symbolized by the inverse sign, e.g., $sin^{-1}$.

Also, if you are not allowed to use a calculator, the you can use a "unit circle" for common angles.

3. 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 $
\sin{x} = \frac{1}{2}
$

using a special right triangle, but how can you get sinx=-4 using that technique?

4. 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.

Patrick

5. Thanks a lot, this is really helpful. I think I just have one more question, and that is how to find $\cos{\frac{\pi}{2}}=x$

6. 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. $\frac{\pi}{2}$ 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...

$\cos{\frac{\pi}{2}} = 0$

Patrick

7. So the best advice for these types of problems is to memorize the unit circle? Thanks for all the help.

8. 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.