Solve.
-Consider the formula T = 591 - 76 cos 2ϴ, where ϴ is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of ϴ for which the value of T will be 577?
A)79.38°
B)39.69°
C)82.38°
D)36.69°

Question

Quizplus · Accepted Answer

To solve for ϴ when T = 577, substitute T with 577 in the equation and solve for ϴ:577 = 591 - 76 cos 2ϴSubtract 591 from both sides:-14 = -76 cos 2ϴDivide both sides by -76:cos 2ϴ = 14/76Simplify:cos 2ϴ = 0.18421Take the inverse cosine (in degrees) of both sides:2ϴ = cos⁻¹(0.18421)2ϴ ≈ 79.38°Divide by 2 to solve for ϴ:ϴ ≈ 79.38° / 2ϴ ≈ 39.69°Thus, the smallest positive value of ϴ to the nearest hundredth of a degree is approximately 39.69°.

Solve. -Consider the Formula T = 591 - 76 Cos 2ϴ