Math141Sols3S11

# Math141Sols3S11 - MIDTERM 3 SOLUTIONS(CHAPTER 4 MATH 141...

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(Intersection points have the same y -coordinate, ± 0.8 .) [Approximate] Solution set: 4.069, 5.356 {} 3) Write sec sin ± 1 x 3 ² ³ ´ µ · ² ³ ´ µ · as an equivalent algebraic expression, as we have done in class. Assume x is in the domain of the expression. (7 points) Let ± = sin ² 1 x 3 ³ ´ µ · ¸ . Then, sin = x 3 . We may assume is acute when we draw our right triangle model using SOH-CAH-TOA. We use the Pythagorean Theorem to find the missing (blue) side length, b : x () 2 + b 2 = 3 2 x 2 + b 2 = 9 b 2 = 9 ± x 2 b = ± x 2 Take "+" root. By SOH-CAH-TOA, cos = Adj. Hyp. , so its reciprocal, sec = Hyp. Adj. . sec sin ± 1 x 3 ² ³ ´ µ · ² ³ ´ µ · = sec ¸ = 3 ± x 2 Warning: 9 ± x 2 ¹ 3 ± x , usually = 39 ± x 2 9 ± x 2
4) An airplane is flying at an altitude of 10,000 feet over a flat desert. In other

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Math141Sols3S11 - MIDTERM 3 SOLUTIONS(CHAPTER 4 MATH 141...

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