Inverse Trig Functions Rita Korsunsky

To find the inverse of function y = sin x: First: check if a function has an inverse function: Use horizontal line test! More than one point of intersection => Function does not pass horizontal line test => No inverse function, BUT…

Sin function is now one to one (passes horizontal line test)!

To graph the inverse reflect function over line y = x. Inverse sin function (Arcsinx or Sin-1x) Domain and Range are switched

Graph of cos x and Arccosx y = Arccos x y = x y = Arccosx y =cos x

Arctan x tan x Arctanx Restrict the domain Reflect over y = x y = x

Graphs of Inverse Trig Functions

Example 1 Example 2

Example 3 Find the exact value of If the value inside of arcsin, arccos or arctan is positive, the angle will always be in the I quadrant, so the answer will be: The REFERENCE ANGLE

Example 4

Example 5

Example 6 Arctan (-1) = x. Find x

Example 7 Cos x = ? positive 2 x 3

Example 8 Need to find sin of the angle where tan=

Example 9 Need to find tan of angle where sin=

Example 10

Graphing