Solve the problem.
-Consider the formula $T = 591 - 76 \cos 2 \theta$, 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 567?

Question

Quizplus · Accepted Answer

To solve for $\theta$, first set $T = 567$ and solve the equation $567 = 591 - 76 \cos 2 \theta$. Rearranging gives $\cos 2 \theta = \frac{591 - 567}{76}$, which simplifies to $\cos 2 \theta = \frac{24}{76}$ or $\cos 2 \theta = 0.3158$. Taking the inverse cosine (and remembering to divide by 2 because of the $2\theta$) gives $\theta = \frac{1}{2} \cos^{-1}(0.3158)$, which calculates to approximately $35.79^\circ$.

Solve the Problem T=591−76cos⁡2θT = 591 - 76 \cos 2 \thetaT=591−76cos2θ

Solve the Problem $T = 591 - 76 \cos 2 \theta$