L3 Derivatives of Primary and Reciprocal Trigonometric Functions - Part 1
Completion requirements
Unit 4B
Trigonometry Part 2
Lesson 3: Derivatives of Primary and Reciprocal Trigonometric Functions
In this Lesson, you will learn about the derivatives of the sine and cosine functions. Before getting into the derivatives algebraically, take a look at them graphically using the Sine and Cosine Derivatives applet.
Interactive
Click the interactive button to open the Sinusoidal and Cosine Derivatives applet.
- The applet shows a graph of the sine function. There is a point on the graph that can be moved.
- Click “Show Slope”. The value of the slope of the sine function at the blue point is represented by the red point. When the slope of the sine function is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«/mrow»«/mstyle»«/math», the red point has a «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-coordinate of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn»0«/mn»«mo».«/mo»«mn»5«/mn»«/mrow»«/mstyle»«/math».
- What happens to the red point as you move the blue point?
- Click “Trace Slope” to graph the slope for different «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-values. The result is the derivative function. Do you recognize it?
- Click "«math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»y«/mi»«mo»=«/mo»«mi»cos«/mi»«mi»x«/mi»«/mrow»«/mstyle»«/math»" and repeat the exercise. Do you recognize the derivative function for «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»y«/mi»«mo»=«/mo»«mi»cos«/mi»«mi»x«/mi»«/mrow»«/mstyle»«/math»?