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The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is -1.4 .
Which is the principal value of
tan^(-1)(-1.4) ?
Choose 1 answer:
(A) -4.09
(B) -0.95
(C)
2.19
(D) 5.33

The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is $-1$ . $4$ . $\newline$ Which is the principal value of $\tan ^{-1}(-1.4) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\quad-4.09$ $\newline$ (B) $-0$ . $95$ $\newline$ (C) $\mathbf{2 . 1 9}$ $\newline$ (D) $5$ . $33$

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Calculate mean absolute deviation

Full solution

Q. The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is

-1

.

4

.

\newline

Which is the principal value of

\tan ^{-1}(-1.4) ?

\newline

Choose

1

answer:

\newline

(A)

\quad-4.09

\newline

(B)

-0

.

95

\newline

(C)

\mathbf{2 . 1 9}

\newline

(D)

5

.

33

Determine angle in radians: To find the principal value of $\tan^{-1}(-1.4)$ , we need to determine the angle in radians whose tangent is $-1.4$ and lies in the range of the inverse tangent function, which is between $-\pi/2$ and $\pi/2$ .
Calculate inverse tangent: Using a calculator or inverse tangent function, we calculate $\tan^{-1}(-1.4)$ . The calculator should be set to radians mode for this calculation.
Obtain calculated value: The calculator gives us the value of $\tan^{-1}(-1.4)$ as approximately $-0.9505$ radians when rounded to the nearest hundredth.
Compare with options: Comparing the calculated value with the options given, we find that option (B) $-0.95$ is the closest to our calculated value and falls within the range of the inverse tangent function.
Identify principal value: Therefore, the principal value of $\tan^{-1}(-1.4)$ is $-0.95$ radians, which corresponds to option $(B)$ .

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