SOLUTION: If cos(A) = -5/13, where pi/2 is less than or equal to A < pi, then evaluate cos(A-(pi/4))

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Question 934032: If cos(A) = -5/13, where pi/2 is less than or equal to A < pi, then evaluate cos(A-(pi/4))
Answer by lwsshak3(11628) About Me  (Show Source):
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If cos(A) = -5/13, where pi/2 is less than or equal to A < pi, then evaluate cos(A-(pi/4))
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sin(A)=12/13 (working with a (5-12-13) reference right triangle in quadrant II)
reference angle A is in quadrant II
cos(x-y)=cosxcosy+sinxsiny
cos(A-(π/4))=cosAcos(π/4)+sinAsin(π/4)
=-5/13*(√2/2)+12/13*√2/2
=-5√2/26+12√2/26=7√2/26
cos(A-(pi/4))=7√2/26