Question 1194933
 
Use a half - angle identity to find the exact value of each expression.

so, identities you need are:

{{{sin(theta/2)=sqrt((1-cos(theta))/2)}}}

{{{cos(theta/2)=sqrt((1+cos(theta))/2)}}}

{{{tan(theta/2)=sin(theta)/(cos(theta) + 1)}}}



5) {{{tan 45°}}}

{{{theta/2=45}}}° =>{{{theta=90}}}°

{{{tan(45)=sin(90)/(cos(90) + 1)}}}........{{{sin(90)=1}}}, {{{cos(90) =0}}}

{{{tan(45)=1/(0 + 1)}}}

{{{tan (45)= 1}}} 



6) {{{sin 165}}}°

{{{(theta/2)=165}}}° =>{{{theta=330}}}


{{{sin(165)=sqrt((1-cos(330))/2)}}}


{{{sin(165)=sqrt((1-sqrt(3)/2)/2)}}}


{{{sin(165)=sqrt(((1/2) (2 - sqrt(3)))/2)}}}

{{{sin(165)=(sqrt(3) - 1)/(2 sqrt(2))}}}



7) {{{sin (5pi/6)}}}


{{{theta/2=(5pi/6)}}} =>{{{theta=2(5pi/6) =(5pi/3) }}}


{{{sin(5pi/6)=sqrt((1-cos(5pi/3))/2)}}}


{{{sin(5pi/6)=sqrt((1/2)/2)}}}


{{{sin(5pi/6)=sqrt(1/4)}}}


{{{sin(5pi/6)=1/2}}}



8.  {{{cos(30)}}}°

{{{theta/2=30}}} =>{{{theta=60 }}}


{{{cos(30)=sqrt((1+cos(60))/2)}}}


{{{cos(30)=sqrt((1+1/2)/2)}}}


{{{cos(30)=sqrt(3/4)}}}


{{{cos(30)=sqrt(3)/2}}}