Sin α β sin α cos β cos α sin β 5 3 12 1226 cos

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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( β ) = (12 3 1/2 + 5)/26
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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) 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. x = ( α + β )/2 and y = ( α - β )/2 quickly, easily.
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