Find the exact value of cos 210 using the half angle formula?

1 Answer
Jim G.
Feb 27, 2018

#cos210=-sqrt3/2#

Explanation:

#"note that "420/2=210#

#x/2=210rArrx=420#

#"using the "color(blue)"half angle formula"#

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

#rArrcos210^@=+-sqrt((1+cos420^@)/2)#

#210^@" is in the third quadrant where "cos210^@<0#

#rArrcos210^@=-sqrt((1+cos60^@)/2)#

#color(white)(rArrcos210^@)=-sqrt((1+1/2)/2)#

#color(white)(rArrcos210^@)=-sqrt(3/4)=-sqrt3/2#

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