Question 825698
I'm going to use x in place of θ (it's easier to type)


sec(x) = 4/5


1/cos(x) = 4/5


cos(x) = 5/4 ... take the reciprocal of both sides


cos^2(x) = 25/16 ... square both sides


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sin^2(x) + cos^2(x) = 1


sin^2(x) + 25/16 = 1


sin^2(x) = 1 - 25/16


sin^2(x) = 16/16 - 25/16


sin^2(x) = (16 - 25)/16


sin^2(x) = -9/16


sin(x) = sqrt(-9/16)


As you can see in the last step above, we have sqrt(-9/16), but we cannot take the square root of a negative number and get a real number as a result. So this leads me to think that there's a typo somewhere. Please double check. Thanks.