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 $\mathrm { T }$ will be 559 ?
A) $68.10 ^ { \circ }$
B) $29.55 ^ { \circ }$
C) $32.55 ^ { \circ }$
D) $65.10 ^ { \circ }$

Question

Quizplus · Accepted Answer

First, set the equation $591 - 76 \cos 2 \theta = 559$ and solve for $\cos 2 \theta$. Subtracting 591 from both sides gives $-76 \cos 2 \theta = -32$, and dividing by -76 gives $\cos 2 \theta = \frac{32}{76}$ or $\cos 2 \theta = \frac{2}{19}$. Taking the cosine inverse of both sides gives $2 \theta = \cos^{-1}(\frac{2}{19})$, and dividing by 2 gives $\theta = \frac{1}{2} \cos^{-1}(\frac{2}{19})$. Calculating this gives a value close to $32.55^\circ$, which is the smallest positive value of $\theta$ that satisfies the equation.

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

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