Question 1203872
{{{ cot(alpha) = 3}}}

Use the definition of cotangent to find the known sides of the unit circle


{{{ cot(alpha) = adj/opp }}}

so, 

{{{ adj/opp=3}}}

which is same as

{{{ adj/opp=3/1}}}

so, {{{ adj=3}}}  and{{{  opp=1}}}


then hypothenuse is:

{{{  hyp=sqrt(adj^2+opp^2)}}}
{{{  hyp=sqrt(3^2+1^2)}}}
{{{  hyp=sqrt(10)}}}



(a)

{{{  tan(alpha)=opp/adj}}}


{{{  tan(alpha)=1/3}}}


(b)

{{{ csc(alpha)=hyp/opp }}}


{{{ csc(alpha)=sqrt(10)/1}}}


{{{  csc(alpha)=sqrt(10)}}}



(c)



{{{ sec(alpha)=hyp/adj}}}


{{{  sec(alpha)=sqrt(10)/3}}}



(d)


{{{ sin(alpha)=opp/hyp }}}


 {{{ sin(alpha)=1/sqrt(10)}}}


{{{ sin(alpha)=sqrt(10)/10}}}