Find the exact value of the following under the given conditions a.cos(a-b) b.(a-b) c.tan(a-b)

Question

cos b=9/17, 0<β<pi/2

sin a =-60/61, pi<β<3pi/2

Answer 1

cosb = 9/17 = 0.5294

b = arcos(0.5294) = 58.035 degrees in 1st quadrant

sina=60/61 = 0.9836

a = arcsin(0.9836) = 79.609 in 1st quadrant. We want the 3rd quadrant but there is no positive sine in the 3rd quadrant. All signs of sine are negative between pi and 3pi/2 No solution.

a) cos(a-b) = cos(58.035-79.609) = cos(-21.564) = cos(21.564) = 0.9300, but if there no answer to angle a there's no answer to part a either

b) a-b = best answer is there's no answer, but -21.546 is 2nd best answer

c) tan(a-b) = tan(-21.546) = tan(180+21.546) = tan(201.546) = -0.3948 but if there is no angle a, then there is no tan(a-b) either. best answer is no solution. 2nd best answer maybe -0.3948