Question 395071
We have


{{{cos(beta)/sin(beta) = 9/7)}}}. This number is positive, so either sine and cosine are both positive or both negative, so the angle is in quadrant III (since it's not in quadrant I).


Hence, {{{cos(beta) = 9/x}}} and {{{sin(beta) = 7/x}}} for some negative number x that we wish to find. By the Pythagorean identity,


{{{81/x^2 + 49/x^2 = 1}}}


{{{130/x^2 = 1}}}


{{{x^2 = 130}}}


{{{x = -sqrt(130)}}} --> {{{cos(beta) = -9/sqrt(130) = -9sqrt(130)/130}}} and {{{sin(beta) = -7/sqrt(130) = -7sqrt(130)/130}}}.