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Chapter 5: Q 8. (page 495)
Double-angle identities: Use double-angle identities to rewrite each of the following trigonometric expressions until no exponents are involved.
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Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withor ? Why do we need to think about the unit circle after trigonometric substitution with ?
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
Domains and ranges of inverse trigonometric functions: For each function that follows, (a) list the domain and range, (b) sketch a labeled graph, and (c) discuss the domains and ranges in the context of the unit circle.
Solve the integral
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
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