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Unformatted text preview: 1. (10 points) Give a table that gives the exact values AND decimal approximations, rounded to the nearest hundredth, for sin α, cos α and tan α for α = 0 ◦ , α = 30 ◦ , α = 45 ◦ , α = 60 ◦ and α = 90 ◦ . Also give the radian measures of all the angles. 2. (10 points) Use the reference angle principle (and your table above) to give the exact value of the following: (a) cos 135 ◦ (b) tan( 5 π 6 ) 1 3. (10 points) Use the sum/difference formulas to do the find the exact value of sin 75 ◦ 4. (10 points) Show that sin 2 x sin 4 x = cos 2 x cos 4 x for all x , i.e. show that the equation is an identity. 2 5. (20 points) Consider the function f ( x ) = ( x 1) 3 1. (a) (4 points) Show that the function f ( x ) is onetoone. (You can do this alge braically or graphically) (b) (8 points) Find the equation of f 1 ( x ). (c) (8 points) Graph both f ( x ) and f 1 ( x ) in the same coordinate system. 3 6. (20 points) This problem is about modeling population growth with functions: Assume in both parts Mathland has 100 inhabitants now and 110 inhabitants exactly one year...
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 Spring '08
 STAFF
 Approximation, Angles, Mathland

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