Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ). Write solutions as exact values or to four decimal places, as
appropriate.
-Consider the formula $\mathrm { T } = 591 - 76 \cos 2 \theta$, where $\theta$ is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of $\theta$ for which the value of $T$ will be 640 ?

Question

Quizplus · Accepted Answer

First, set $T = 640$ and solve for $\theta$: $640 = 591 - 76 \cos 2 \theta$. This simplifies to $\cos 2 \theta = - \frac{49}{76}$. Solving for $2 \theta$ gives $2 \theta = \cos^{-1} \left(- \frac{49}{76}\right)$, which yields two solutions in the given interval due to the periodic nature of the cosine function. The smallest positive solution for $\theta$ is approximately $65.07^\circ$.

Solve the Equation for Solutions Over the Interval [0 [0,2π)[ 0,2 \pi )[0,2π)

Solve the Equation for Solutions Over the Interval [0 $[ 0,2 \pi )$