2.9 Derivatives of the Trigonometric Functions
By the end of your studying, you should know:
On-screen applet instructions: Use the slider to let x → 0. What is the limit of sin(x)/x as x → 0?
ExamplesConsider the picture below:
θ is the central angle of the circle, s is the arc intercepted by θ, and d is the chord defined by θ. Find
A pilot flying at 3 miles above the ground at 600 miles per hour sights the airport with a spotting scope. How fast must she turn the scope when the angle between the path and plane is 40o to keep the scope pointed at the airport?
A block at the end of a spring is stretched past its rest position and released. Its position at time t is given by the formula d(t) = 4cos(t). Find the velocity of the spring at time t. When does the block move fastest?
AppletsLimit of sin(x)/x as x approaches 0
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 2.9 Derivatives of the Trigonometric Functions (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Nothing yet has been found. Any ideas?
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel