Question

Solve each question in the interval from 0to 2 pi. Round your answer to the nearest hundredth. 3cos4theta=-2

Answer 1

\[3 \cos(4 \theta)=-2 \\ \cos(4 \theta)=\frac{-2}{3} \\ \text{ let } u=4 \theta \\ 0 < \theta <2 \pi \\ \text{ but } \theta=\frac{u}{4} \\ \text{ so we have the inequality in terms of } u \text{ is } \\ 0< \frac{u}{4}<2 \pi \\ \text{ multiplying 4 on all sides } \\ 0<u<8 \pi\]

So try to solve first:
\[\cos(u)=\frac{-2}{3} \text{ where } 0<u < 8 \pi\]
Then we will come back and solve for theta

Answer 2

u=2.30?

Answer 3

That is an approximation for one solution
for u
You still have like 4 more solutions.

Answer 4

oh ok