1 sin α cos α cos α 1 sin α test 02mac1114 page 3

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1 - sin( α ) cos( α ) = cos( α ) 1 + sin( α )
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TEST-02/MAC1114 Page 3 of 4 6. (5 pts.) Obtain the exact value of cos( π /8). Show clearly and neatly all the uses of appropriate identities. cos( π /8) = 7. (5 pts.) If csc( θ ) = 4 and cos( θ ) < 0, what is the exact value of sin(2 θ ) ?? Show clearly and neatly all your uses of appropriate identities. sin(2 θ ) = 8. (5 pts.) Express the following product as a sum containing only sines or cosines. sin(5 θ )cos(3 θ ) = 9. (10 pts.) Find the exact value of each of the following expressions if tan( α ) = -5/12 with π /2 < α < π and sin( β ) = -1/2 with π < β < 3 π /2. Show all your uses of appropriate identities. sin( α - β ) = cos( α + β ) =
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TEST-02/MAC1114 Page 4 of 4 10. (20 pts.) Time to pay the piper .... Give the exact values for the following: (a) sin(0) = (b) sin( π /6) = (c) sin( π /4) = (d) sin( π /3) = (e) sin( π /2) = (f) cos(0) = (g) cos( π /6) = (h) cos( π /4) = (i) cos( π /3) = (j) cos( π /2) = 11. (10 pts.) In order to get a neat identity for cos( α ) + cos( β ), one begins with the identity (*) cos(x + y) + cos(x - y) = 2 cos(x)cos(y) and sets x + y = α and x - y = β in the left side of the identity. To make the substitution uniform, it is necessary to replace the "x" and "y" on the right side of (*) with what they are in terms of " α " and " β " in the system of linear equations x + y = α x - y = β . Solve for x and y in this system.
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