<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
You are viewing an older version of this Study Guide. Go to the latest version.

Inverses by Mapping

Reflect points from f(x) across the line y = x.

Atoms Practice
%
Progress
 
 
 
MEMORY METER
This indicates how strong in your memory this concept is
Practice
Progress
%
Practice Now
Turn In
Inverse of Trigonometric Ratios

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.

 one to one function is a function that passes both the horizontal and vertical line tests.

License: CC BY-NC 3.0

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.

Explore More

Sign in to explore more, including practice questions and solutions for Definition of the Inverse of Trigonometric Ratios.
Please wait...
Please wait...