How do you use the quadratic formula to solve #8cos^2theta-7costheta+1=0# for #0<=theta<360#?

1 Answer
Jul 13, 2017

#"see explanation"#

Explanation:

#"let " x=costheta#

#rArr8cos^2theta-7costheta+1=0#

#-=8x^2-7x+1=0#

#"solve using the "color(blue)"quadratic formula"#

#"with " a=8,b=-7,c=1#

#rArrx=(7+-sqrt(49-32))/16=7/16+-1/16sqrt17#

#rArrcostheta=7/16+1/16sqrt17" or " costheta=7/16-1/16sqrt17#

#rArrcostheta=0.6952" or " costheta=0.1798#

#rArrtheta=45.96^@" or " theta=79.64^@#

#"these are the "color(blue)"related acute angles"#

#"since " theta>0" in both cases then "theta" lies in"#
#"quadrants 1 and 4"#

#theta=45.96" or "theta=(360-45.96)#

#rArrtheta=45.96" or "314.04#

#color(red)"Also"#

#theta=79.64" or "theta=(360-79.64)#

#rArrtheta=79.64" or " 280.36#

#color(blue)"the solutions are"#

#theta=45.96^@,79.64^@,280.36^@,314.04^@to[0,360)#