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The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is -21 .
Which is the principal value of
tan^(-1)(-21) ?
Choose 1 answer:
(A) -1.52
(B) 1.62
(C) 4.76
(D) 7.90

The following are all angle measures (in radians, rounded to the nearest hundredth) whose tangent is $-21$ . $\newline$ Which is the principal value of $\tan ^{-1}(-21)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-1$ . $52$ $\newline$ (B) $1$ . $62$ $\newline$ (C) $4$ . $76$ $\newline$ (D) $7$ . $90$

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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

-21

.

\newline

Which is the principal value of

\tan ^{-1}(-21)

?

\newline

Choose

1

answer:

\newline

(A)

-1

.

52

\newline

(B)

1

.

62

\newline

(C)

4

.

76

\newline

(D)

7

.

90

Consider the range: To find the principal value of the inverse tangent function, we need to consider the range of the arctangent function, which is from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ radians. The principal value is the angle in this range whose tangent is $-21$ .
Use calculator to find arctangent: We can use a calculator to find the arctangent of $-21$ . Since the tangent function is negative in the second and fourth quadrants, and the principal value must be in the range from $-\pi/2$ to $\pi/2$ , the answer will be in the fourth quadrant.
Answer in fourth quadrant: Using a calculator to find $\tan^{-1}(-21)$ , we get an angle in radians. The calculator will give us the value in the fourth quadrant because it's negative.
Principal value in range: The calculator gives us an angle of approximately $-1.52$ radians. This is the principal value because it is within the range of $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ .

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