Question

solve for theta. cos(2θ) +4 = 5cosθ

Answer 1

27.5

Answer 2

how did you do that?

Answer 3

like the steps

Answer 4

Use a trig identity to express \(\cos2\theta\) in terms of \(\theta\), then solve the resulting quadratic for \(\cos\theta.\)

Answer 5

hmmmm let me try that out

Answer 6

still not grasping it

Answer 7

Look up an identity for \(\cos2\theta\)!

Answer 8

cos^2θ - sin^2θ

Answer 9

OK! Now eliminate \(\sin^2θ\) using \(\sin^2θ=1−\cos^2θ\).

Answer 10

ok....

Answer 11

Then substitute back in the original expression and you get a quadratic equation in \(\cos\theta\).

Answer 12

\[\cos 2x+4=5\cos x\]
\[2\cos ^2x-1+4=5\cos \]
\[2\cos ^2x-5\cos x+3=0\]
\[(2\cos x-3)(\cos x-1)=0\]
\[\cos x=\frac{3}{2}, discard\]
\[\cos x=1\]
x=0