Unformatted text preview: MAC1114 - Homework 9
Due Thursday, March 17
1. Find the asymptotes (do not nd periods or sketch graphs) of the following functions:
(a) 2 csc(3x − π )
(b) sec( π x + π ) + 3
(c) 1 tan( 2 x − π )
(d) − cot(7x − 3)
2. In the gure below, a square is inscribed in another square, and then a circle is inscribed in the smaller
square. Point P is the center of the circle. The area of the larger square is 100. Find the area of the
region shaded blue. (optional: If you're really industrious, try nding the area shaded green. It's an
extremely dicult problem, but wrangling with it will build character) 3. Find sin(arccos(tan(arcsin(3y )))).
4. Simplify: log | cos2 x| − log |1 + sin x| + log | cot x|
5. Verify the identity: tan2 x − sec2 x
= (sin x − 1) sec x.
1 + sin x 1 ...
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