Given cos(2α)=−47/81 and π/2<2α<π, find exact values of the six trigonometric functions.
Note: You are not allowed to use decimals in your answer.
sin(α) = ................
cos(α) = ........................
tan(α) = ......................
csc(α) = .
sec(α) = .....................
cot(α) = ........................
Note: You are not allowed to use decimals in your answer.
sin(α) = ................
cos(α) = ........................
tan(α) = ......................
csc(α) = .
sec(α) = .....................
cot(α) = ........................
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cos(2a)=-47/81
cosa^2-sina^2=-47/81
1-2sina^2=-47/81
-2sina^2=-128/81
sina^2=64/81
sina=8/9 = 0.89
now sina^2+cosa^2=1
therefore 64/81 + cosa^2=1
cosa^2=17/81
cosa=sqrt17/9
tana=8/9*9/sqrt17 = 8sqrt17
csca=1/sina = 1/8/9 = 9/8
seca=1/cosa=1/sqrt17/9 = 9/sqrt17
cota=1/tana=1/8sqrt17
cosa^2-sina^2=-47/81
1-2sina^2=-47/81
-2sina^2=-128/81
sina^2=64/81
sina=8/9 = 0.89
now sina^2+cosa^2=1
therefore 64/81 + cosa^2=1
cosa^2=17/81
cosa=sqrt17/9
tana=8/9*9/sqrt17 = 8sqrt17
csca=1/sina = 1/8/9 = 9/8
seca=1/cosa=1/sqrt17/9 = 9/sqrt17
cota=1/tana=1/8sqrt17