REMEMBER: This connects with trigonometric functions so click here for a refresher on trig function and inverses.
The trigonometric inverse is a function that undoes a trig function to give the original argument of the function. It can also be used to find an angle from the ratio of two sides.
Caution: The trigonometric inverse is not the same as the sec, csc, and cotangent.
Exact Values for Inverse sine, cosine, and tangent
To find the exact valued you need to know the Unit Circle, click here
Solution: This is a value from the special right triangles and the unit circle.
Recall that is from the triangle. The reference angle for and would be . Because this is sine and it is negative, it must be in the third or fourth quadrant. The answer is either or .
Inverse of Functions Through Algebraic Manipulation
The horizontal line test is a test applied to a function to see how many times the graph of a function intersects an arbitrary horizontal line drawn across the coordinate grid. A function passes this test if it intersects the horizontal line in only one place, no matter where the horizontal line is drawn.
A one to one function is a function that passes both the horizontal and vertical line tests.
The vertical line test is a test applied to a function to see how many times the graph of a function intersects an arbitrary vertical line drawn across the coordinate grid. A function passes this test if it intersects the vertical line in only one place, no matter where the vertical line is drawn.
What do you need to do the the regular function to find the inverse of it? Click here for guidence.
Inverse by Mapping
Mapping is a procedure involving the plotting of points on a coordinate grid to see the behavior of a function.
The points and in the coordinate plane are symmetric with respect to the line .
The points and are reflections of each other across the line .
Remember: Not all inverses of a function will be functions.