# HW5sol - MAC1114 Homework 5 Due Tuesday February 15 1 Find...

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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)=undened 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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