Penny needs to find cos #pi/12#. If she only knows that cos #pi/6 = sqrt(3)/2#, how can she find cos #pi/12# using a double angle formula? What is her answer?

Penny needs to find cos #pi/12#. If she only knows that cos #pi/6 = sqrt(3)/2#, how can she find cos #pi/12# using a double angle formula? What is her answer?

1 Answer
Jim G.
Dec 17, 2017

#cos(pi/12)=1/2sqrt(sqrt3+2)#

Explanation:

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

#•color(white)(x)cos2A=2cos^2A-1#

#rArrcos(pi/6)=2cos^2(pi/12)-1#

#rArr2cos^2(pi/12)=cos(pi/6)+1#

#color(white)(xxxxxxxxxx)=sqrt3/2+1=1/2(sqrt3+2)#

#rArrcos^2(pi/12)=1/4(sqrt3+2)#

#rArrcos(pi/12)=+-sqrt(1/4(sqrt3+2)#

#"since "pi/12" is acute then"#

#cos(pi/12)=1/2sqrt(sqrt3+2)#

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