Inverse Trigonometric Functions

1. Show that the function is one-to-one. Graphing does not count as proof. (Hint: Use the derivative of the function.)

 

2. Find a formula for the inverse function of . Verify that

 

3. Fill in the values of and for . Provide detail to support your answers.

 

x

 

4. In the triangle below, angle is (a) the arcsine of what number? (b) the arctangent of what number? (c) the arcsecant of what number? (d) the arccosine of what number?

3

4

5. Calculate the derivatives.

(a)

(b)

(c)

6. Evaluate each integral based on inverse trigonometric functions. An answer with no sufficient detail will not receive full credits.

(a)

(b)

(c)