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Unformatted text preview: MAC1114  Homework 5
Due Tuesday, February 15
1. Find the period and asymptotes and sketch a graph of the following functions:
(a) 3
2 cot(2x − π )
Period: π = π
b
2 Asymptotes: nπ = 2x − π ⇒ (n + 1)π = 2x ⇒ kπ
2 = x, k ∈ Z Graph:
(b) sec(πx − π ) + 1
2
π
π
Period: 2b = 2π = 2
Asymptotes: nπ + π = πx −
2 π
2 ⇒ nπ + π = πx ⇒ k = x, k ∈ Z Graph:
2. Evaluate the following:
(a) arcsin(1)=
√ π
2 (b) arcsin(− 22 )= − π
4
(c) arccos(0)= π
2
√ (d) arccos( 3)=undened
1
(e) sin arccos( 1 ) (hint: draw a right triangle with an angle θ such that cos θ = 3 )
3
Your triangle should have adjacent side 1 and hypotenuse 3. The opposite side is found with the
√
√
Pythagorean theorem: 12 + b2 = 32 ⇒ b = 8. Hence sin θ = 38 . 1 ...
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This note was uploaded on 06/10/2011 for the course MAC 1114 taught by Professor Gentimis during the Spring '11 term at University of Florida.
 Spring '11
 Gentimis
 Algebra, Asymptotes

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