Question 926992
Find the exact values of sin(θ/2), cos(θ/2), and tan(θ/2) for the given condition.
csc &#952; = &#8722; 5/4; &#8722;90° < &#952; < 0°
sin(&#952;/2) =
cos(&#952;/2) =
tan(&#952;/2) =
***
reference angle &#952; is in quadrant IV where cos>0, sin<0
csc &#952;=-5/4
sin &#952;=-4/5
cos &#952;=3/5
..
{{{sin(theta)/2
=-sqrt((1-cos(theta))/2)
=-sqrt((1-(3/5))/2)
=-sqrt((2/5)/2)=-sqrt(1/5))}}}
..
{{{cos(theta)/2
=sqrt((1+cos(theta))/2)
=sqrt((1+(3/5))/2)
=sqrt((8/5)/2)=sqrt(4/5))}}}
..
{{{tan(theta)/2=(sin(theta)/2)/(cos(theta)/2)=-sqrt(1/4)=-1/2}}}