# Would someone mind explaining to me why I got this question wrong? Thank you so much for your help!

##### 2 Answers

#### Explanation:

#"using the "color(blue)"half angle identity for cos"#

#•color(white)(x)cos(theta/2)=+-sqrt((1+costheta)/2)#

#"given "pi< theta <(3pi)/2" then"#

#pi/2< theta/2< (3pi)/4larrcolor(blue)"second quadrant"#

#"where "cos(theta/2)<0#

#cos(theta/2)=-sqrt((1-3/5)/2)#

#color(white)(xxxxxx)=-sqrt(1/5)#

#color(white)(xxxxxx)=-1/sqrt5xxsqrt5/sqrt5=-sqrt5/5#

See explanation.

#### Explanation:

Think about it logically.