Question 1203962

If {{{ cos(beta) = -3 / 5 }}} then, without a calculator, find {{{cos(pi / 2 - beta) }}}. Write your answer as a fraction.


use identity: 

{{{cos(pi/2 - beta) =sin(beta)}}}

and 

{{{sin(beta)=sqrt(1-cos^2(beta))}}}


given that


{{{cos(beta) = -3 / 5 }}}, then

{{{cos^2(beta) =( -3 / 5)^2 }}}

{{{cos^2(beta) =9 /25 }}}

substitute in {{{sin(beta)=sqrt(1-cos^2(beta))}}}

{{{sin(beta)=sqrt(1-9 /25 )}}}

{{{sin(beta)=sqrt(16/25 )}}}

{{{sin(beta)=4/5 }}} or {{{sin(beta)= -4/5 }}}


so, {{{cos(pi / 2 - beta) =4/5 }}} or {{{cos(pi / 2 - beta) = -4/5 }}}