Question 1067569
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 If tan &#952; = {{{ 3/2 }}} & cos &#952; < 0, use the fundamental identities to evaluate the remaining five trigonometric functions of theta. 
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If {{{tan(theta)}}} = {{{3/2}}} and {{{cos(theta)}}} < 0,  then the angle {{{theta}}} is in QIII.


Next, {{{sin^2(theta)}}} = {{{1/(1 + (1/tan^2(theta)))}}} is the <U>fundamental identity</U> (which means "Everybody must know it").


Therefore, {{{sin^2(theta)}}} = {{{1 /(1 + (1/(3/2)^2)))}}} = {{{1/(1 + (1/((9/4))))}}} = {{{1/(1+4/9)}}} = {{{1/((13/9))}}} = {{{9/13}}}.

            Hence,  {{{sin(theta)}}} = {{{-sqrt(9/13)}}} = {{{-3/sqrt(13)}}}.    The sign is "-" ("minus") since {{{theta}}} is in QIII.



Further,   {{{cos(theta)}}} = {{{-sqrt(1-sin^2(theta))}}} = {{{-sqrt(1-9/13)}}} = {{{-sqrt(4/13)}}} = {{{-2/sqrt(13)}}}.    The sign is "-" ("minus") since {{{theta}}} is in QIII.



Now you know enough to complete the assignment on your own.


The rest is simply Arithmetic plus knowledge of basic definitions of Trigonometry.
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