Question

Find the solutions of the given equation in the indicated interval. (Give your answers to two decimal places. Enter your answers as a comma-separated list.)

42 (cos(x))^2 + cos(x) -1 = 0 [0,pi]

Answer 1

\[42(\cos (x))^2+\cos (x)-1=0\]

Answer 2

That is a cleaner version of it.

Answer 3

\[42u^2+u-1=0\]
first do you know how to solve this?

Answer 4

42(-1)=-6(7)
1=-6+7
so \[42u^2+7u-6u-1=0\]
factor by grouping
\[7u(6u+1)-1(6u+1)=0\]
\[(6u+1)(7u-1)=0\]
\[u=\frac{-1}{6}, u=\frac{1}{7}\]
so we actually have
\[cosx=\frac{-1}{6}, cosx=\frac{1}{7}\]

Answer 5

\[x=\cos^{-1}(\frac{-1}{6}), x=\cos^{-1}(\frac{1}{7})\]
\[x=1.7, x=1.4\]

Answer 6

oops two decimal spots
\[x=1.74, x=1.43\]