Question 1029080
Substitute {{{u=cos(4*theta)}}}
{{{4u^2+4u-3=0}}}
{{{(2u-1)(2u+3)=0}}}
Two "u" solutions:
{{{2u-1=0}}}
{{{2u=1}}}
{{{u=1/2}}}
So then,
{{{cos(4*theta)=1/2}}}
{{{4*theta=60}}}
{{{4*theta=60+360=420}}}
{{{4*theta=60+720=780}}}
{{{4*theta=60+1080=1140}}}
So,
{{{theta=15}}}
{{{theta=105}}}
{{{theta=195}}}
{{{theta=285}}}
and
{{{4*theta=300}}}
{{{4*theta=300+360=660}}}
{{{4*theta=300+720=1020}}}
{{{4*theta=300+1080=1380}}}
So,
{{{theta=75}}}
{{{theta=165}}}
{{{theta=255}}}
{{{theta=345}}}
8 solutions
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{{{2u+3=0}}}
{{{2u=-3}}}
{{{u=-3/2}}}
{{{cos(4*theta)=-3/2}}}
Since cosine can never equal this value, this u solution does not yield a theta solution.