SOLUTION: find the exact values of six trigonometric functions at a, given that csc((pi/2)-a)=3 in quadrant I?

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Question 868622: find the exact values of six trigonometric functions at a, given that csc((pi/2)-a)=3 in quadrant I?
Answer by lwsshak3(11628) About Me  (Show Source):
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find the exact values of six trigonometric functions at a, given that csc((pi/2)-a)=3 in quadrant I?
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Identity: sin((π/2)-a)=cos a
csc((pi/2)-a)=1/sin((pi/2)-a)=1/cos a=3
cos a=1/3
adjacent side of reference right triangle in quadrant I=√(3^2-1^2)=√(9-1)=√8
sin a=√8/3
sec a=3
csc a=3/√8=3√8/8
tan a=√8
cot a=1/√8=√8/8
..
Calculator check:
cos a=1/3
a≈70.5288˚
csc((pi/2)-a)=1/sin((pi/2)-a)=1/cos(70.5288)≈3.0000…