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The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is 3.7. Which is the principal value of arctan(3.7)? Choose 1 answer: (A) -4.98 (B) -1.83 (C) 1.31 (D) 4.45

The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is 33.77.\newlineWhich is the principal value of arctan⁡(3.7)? \arctan (3.7) ? \newlineChoose 11 answer:\newline(A) −4-4.9898\newline(B) −1-1.8383\newline(C) 11.3131\newline(D) 44.4545

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Full solution

Q. The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is 33.77.\newlineWhich is the principal value of arctan⁡(3.7)? \arctan (3.7) ? \newlineChoose 11 answer:\newline(A) −4-4.9898\newline(B) −1-1.8383\newline(C) 11.3131\newline(D) 44.4545
  1. Find Principal Value: We need to find the principal value of the arctan⁡(3.7)\arctan(3.7), which is the inverse tangent function that returns an angle whose tangent is 3.73.7. The principal value is the unique value of the arctan⁡\arctan function that lies in the interval (−π/2,π/2)(-\pi/2, \pi/2).
  2. Use Calculator: To find the principal value, we can use a scientific calculator or a computational tool that can compute inverse trigonometric functions. We input arctan(3.7)\text{arctan}(3.7) or tan⁡−1(3.7)\tan^{-1}(3.7) to get the result in radians.
  3. Compute Result: After computing arctan⁡(3.7)\arctan(3.7), we get approximately 1.311.31 radians. This is within the interval (−π/2,π/2)(-\pi/2, \pi/2), so it is the principal value.

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