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

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2 Answers
Jim G.
Jun 23, 2018

#-sqrt5/5#

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#

Typo
Jun 23, 2018

See explanation.

Explanation:

Think about it logically. #pi < theta < (3pi)/2#, so #theta# lies in the 3rd quadrant. To get to the 3rd quadrant, you take the basic acute angle and add #pi# or #180^@# to it. If you halve an angle between #pi# and #(3pi)/2#, it will always be greater than #pi/2# because the original angle was greater than #pi# to begin with. Now, realize that since #theta/2# is in the 2nd quadrant, #cos(theta/2)# will always be negative because #costheta# is negative in the 2nd and 3rd quadrant. This is why the correct answer should be #-sqrt5/5#.

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