HW7 Sol - Math 2312 Homework 7 1. Sketch the graph of the...

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Math 2312 Homework 7 1. Sketch the graph of the function for one full period: ±²³ ´ µ¶·¸±¹ º » ¼ ³ . Solution: This is just the function tan x shifted to the right by 4 units. Recall that tan x is pi-periodic, so one period is shown below. x x f tan ) ( 2 x 2 x
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Shifting this graph to the right yields 4 tan ) ( x x f 4 x 4 3 x Note the vertical asymptotes shift 4 units to the right as well. 2. Evaluate the following expressions (without the use of a calculator). a. ±²²³´ µ¶ · . Solution: We are asked to find the angle such that 2 3 cos and note that the range of must be in 0
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The unique angle 6 yields 2 3 6 cos , therefore, 6 2 3 arccos b. ±²³´µ¶·¸¹ Solution: We seek the angle such that sin where is limited to the range 2 2 However, if we note that 1 sin for any and that 1 , then there is no angle that will yield sin
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3. Find the exact value of the expression. a. ±²³´µ¶··¸¹ º » ¼ Solution: Setting 5 3 arccos , then as long as 0 ,this is equivalent to 5 3 cos Setting up a right triangle, 5 4 9 25 3 then, 3 4 tan 5 3 arccos tan b. ½¾ ³¿µ¶·¹ÀÁ Âà ÄŠĺ ÆÇ Solution: Set 13 12 arcsin , then if we’re in the range 2 2 then 13 12 sin Examining the “positive version” È
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13 12 sin on a right trangle, 13 12 5 144 169 so that 12 5 cot 13 12 arcsin cot Now, since
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This note was uploaded on 10/07/2010 for the course MATH 2312 taught by Professor Garrett during the Summer '10 term at Richland Community College.

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HW7 Sol - Math 2312 Homework 7 1. Sketch the graph of the...

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