Two trigonometric inequalities Consider the angle u in
Chapter 2, Problem 90(choose chapter or problem)
Two trigonometric inequalities Consider the angle u in standard position in a unit circle, where 0 u 6 p>2 or -p>2 6 u 6 0 (use both figures). a. Show that _AC_ = _ sin u _, for -p>2 6 u 6 p>2. (Hint: Consider the cases 0 u 6 p>2 and -p>2 6 u 6 0 separately.) b. Show that _ sin u _ 6 _ u _, for -p>2 6 u 6 p>2. (Hint: The length of arc AB is u, if 0 u 6 p>2, and -u, if -p>2 6 u 6 0.) c. Conclude that - _ u _ sin u _ u _, for -p>2 6 u 6 p>2. d. Show that 0 1 - cos u _ u _, for -p>2 6 u 6 p>2.
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