Question 1144167
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The fact that  θ=cos^-1(-4/5)  means  that  cos(θ) = {{{-4/5}}}  and {{{theta}}} in the angle in QII.


Then  csc(θ) = {{{1/sin(theta)}}} = {{{1/sqrt(1-cos^2(theta))}}} = {{{1/sqrt(1 - (-4/5)^2)}}} = {{{1/sqrt(1 -16/25))}}} = {{{1/sqrt(9/25)}}} = {{{1/((3/5))}}} = {{{5/3}}}.    <U>ANSWER</U>
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Notice that the final answer is positive, since both sine and csc functions are positive in QII.