Chapter 5: Q 5. (page 495)
Use Pythagorean identities to rewrite each of the following trigonometric expressions.
Short Answer
The result is.
Chapter 5: Q 5. (page 495)
Use Pythagorean identities to rewrite each of the following trigonometric expressions.
The result is.
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Show that if , then , in the following two ways: (a) by using implicit differentiation, thinking of as a function of , and (b) by thinking of as a function of .
For each function u(x) in Exercises 9โ12, write the differential du in terms of the differential dx.
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
Explain how to know when to use the trigonometric substitutions , Describe the trigonometric identity and the triangle that will be needed in each case. What are the possible values for and in each case?
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