Inverse Trigonometric Functions
Neil Trivedi
Teacher
Inverse Trigonometric Functions
There are two types of functions: one-to-one and many-to-one. Only a one-to-one function can have an inverse. However, all trigonometric functions are many-to-one. Therefore, we must restrict the domain to make a trigonometric function one-to-one. The restricted domain depends on the function.
For inverse trigonometric functions, we will be using ‘arc’ to describe them (it comes from arcs in a circle). Therefore, instead of saying , we will instead say .
Domain: Range: Domain: Range:
Domain: Range: Domain: Range:
Domain: Range: Domain: Range:
Example 1:
a) Work out the value of in terms of .
Single Step: Input value in the inverse cosine function.
b) Solve the equation
Single Step: Solve the equation.
Rearranging gives ,
Take on both sides to eliminate ,
No answer provided.
Example 2:
Show that,
Single Step: Let and find
Take on both sides of to get
We can construct a triangle with the given information using SOHCAHTOA with being the adjacent side and being the hypotenuse. Applying Pythagoras' theorem we can find the third side has length .
From the diagram, we can see that .
Therefore, we have by substituting .
No answer provided.
Challenging Questions