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4 15 12 8 8 5 pts express the following product as a

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)cos( θ ) = 2 (1/4) (-15 1/2 /4) = -15 1/2 /8 8. (5 pts.) Express the following product as a sum containing only sines or cosines. sin(5 θ )cos(3 θ ) = (1/2)[sin(8 θ ) + sin(2 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 ) = 5/13 and cos(a) = -12/13 since π /2 < α < π . cos( β )=- 3 1/2 /2 since π < β <3 π /2. sin( α - β ) = sin( α )cos( β ) - cos( α )sin( β ) = -(5 3 1/2 + 12)/26 cos( α + β ) = cos( α )cos( β ) - sin( α )sin(
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TEST-02/MAC1114 Page 3 of 3 10. (20 pts.) Time to pay the piper. ... Give the exact values for the following: (a) sin(0) = 0 (b) sin( π /6) = 1/2 (c) sin( π /4) = 2 1/2 /2 (d) sin( π /3) = 3 1/2 /2 (e) sin( π /2) = 1 (f) cos(0) = 1 [You could use the Complementary Angle Theorem to get the cosines, folks. LOOK !] (g) cos( π /6) = 3 1/2 /2 (h) cos( π /4) = 2 1/2 /2 (i) cos( π /3) = 1/2 (j) cos( π /2) = 0 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) a n ds e t sx+y= α a n dx-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. x=( α
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4 15 12 8 8 5 pts Express the following product as a sum...

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