None of the six basic trigonometry functions is a one-to-one function. However, in the following list, each trigonometry function is listed with an appropriately restricted domain, which makes it one-to-one.

- for
- for
- for
- for , except
- for , except
*x*= 0 - for

- for
- for
- for
- arc for , except
- arc for , except
*y*= 0 - arc for

- arc
- arc
- arc

*PROBLEM 1 :*Differentiate .Click HERE to see a detailed solution to problem 1.

*PROBLEM 2 :*Differentiate .Click HERE to see a detailed solution to problem 2.

*PROBLEM 3 :*Differentiate arc arc .Click HERE to see a detailed solution to problem 3.

*PROBLEM 4 :*Let arc . Solve*f*'(*x*) = 0 for*x*.Click HERE to see a detailed solution to problem 4.

*PROBLEM 5 :*Let . Show that*f*'(*x*) = 0 . Conclude that .Click HERE to see a detailed solution to problem 5.

*PROBLEM 6 :*Evaluate .Click HERE to see a detailed solution to problem 6.

Some of the following problems require use of the chain rule.

*PROBLEM 7 :*Differentiate .Click HERE to see a detailed solution to problem 7.

*PROBLEM 8 :*Differentiate .Click HERE to see a detailed solution to problem 8.

*PROBLEM 9 :*Differentiate .Click HERE to see a detailed solution to problem 9.

*PROBLEM 10 :*Determine the slope of the line tangent to the graph of at*x*=*e*.Click HERE to see a detailed solution to problem 10.

*PROBLEM 11 :*Differentiate arc . What conclusion can be drawn from your answer about function*y*? What conclusion can be drawn about functions arc and ?Click HERE to see a detailed solution to problem 11.

*PROBLEM 12 :*Differentiate .Click HERE to see a detailed solution to problem 12.

*PROBLEM 13 :*Find an equation of the line tangent to the graph of at*x*=2 .Click HERE to see a detailed solution to problem 13.

*PROBLEM 14 :*Evaluate .Click HERE to see a detailed solution to problem 14.

*PROBLEM 15 :*A movie screen on the front wall in your classroom is 16 feet high and positioned 9 feet above your eye-level. How far away from the front of the room should you sit in order to have the ``best" view ? (HINT: Find the largest possible angle in the given diagram below.)Click HERE to see a detailed solution to problem 15.

Click HERE to see a detailed solution to problem 15.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

Tue Sep 16 11:30:08 PDT 1997