Unformatted text preview: MAC1114  Homework 7
Due Tuesday, March 1
1. Write the following in a form with no fractions:
1
1 + cos x
cos2 x
(b)
1 − sec x (a) 2. Write as a single logarithm and simplify: log3 (cos2 x) + log3 (sec2 x + csc2 x) + log3 (sin2 x)
2
3. Use the trigonometric substitution x = 3 tan θ, for 0 < θ < π , to rewrite the equation
2
as a function of θ, and nd cos θ (you will need to draw a triangle). √ √ 9x2 + 4 = 3 4. Consider the equation 9x2 − 16 = 5. There is a trigonometric substitution that turns this equation
into something of the form ___(θ) = 5, where the blank is lled in with one of the six trig functions
(sin, cos, etc.). Find the appropriate trig substitution that accomplishes this, and explain (using words,
and equations if necessary) the thought process you used to come up with your answer. The more
complete and logical your explanation, the better. 1 ...
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 Spring '11
 Gentimis
 Algebra, Trigonometry, Fractions, appropriate trig substitution

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