diff --git a/education/math/MATH1060 (trig)/Graphing.md b/education/math/MATH1060 (trig)/Graphing.md index ced1392..fbbcf91 100644 --- a/education/math/MATH1060 (trig)/Graphing.md +++ b/education/math/MATH1060 (trig)/Graphing.md @@ -125,6 +125,8 @@ The inverse of a trig function is **not** the same as the reciprocal of a trig f - To find the inverse of cos, you need to restrict the domain to $[0, \pi]$ - To find the inverse of tangent, you need to restrict the domain to $(-\frac{\pi}{2}, \frac{\pi}{2})$. +The graphs of an inverse function can be found by taking the graph of $f$, and flipping it over the line $y=x$. + # Examples > Given $-2\tan(\pi*x + \pi) - 1$ @@ -145,3 +147,7 @@ Vertical shift: $1$ | Period | $\frac{\pi}{\|\pi\|} = 1$ | | Phase shift | $\frac{-\pi}{\pi} = -1$ | | Vertical shift | $-1$ | +> Evaluate $\arccos{\frac{1}{2}}$ using the unit circle. + +Taking the inverse of the above function, we get this. Because the domain of $cos$ ranges from $0$ to $\pi$ inclusive, the answer is going to be in quadrant 1 or quadrant 2. +$$ cos(x) = \frac{1}{2} $$ \ No newline at end of file