# Derivatives of Basic Trig Functions

- Author:
- Dr. Jack L. Jackson II

- Topic:
- Calculus, Cosine, Derivative, Differential Calculus, Functions, Sine, Trigonometry

## Derivatives of Basic Trigonometric Functions

You should be very familiar with the graphs of these six basic trigonometric functions. Can you predict their shapes and characteristics before you see them graphed?
In the app check the checkboxes in the left column to see the graphs of the six basic trigonometric
functions.
Can you determine the basic shape and graph characteristics of the graphs of the derivatives before you see them graphed?
Check the checkboxes in the second column to see the graphs of the derivatives of these six basic
trigonometric functions.
Based upon these graphs can you determine in advance what the formulas are for these derivative functions?
Check the checkboxes for in the third column to see the formulas displayed.
After investigating them individually display all six derivative rules. Do you see some patterns?
One thing to notice is that if the original function starts with "co" then the derivative has a negative sign.
Also, the derivatives of the cofunctions are found by inserting this negative sign in, along with taking
the cofunctions of the functions in the derivative formula on the left. If you can memorize the rules on
the left of the display, then you should be able to use them to get the derivative formulas on the right.
One at a time, check the checkboxes in the last column to see the algebraic derivations of these derivative
formulas.