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The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is -0.26 .
Which is the principal value of
cos^(-1)(-0.26) ?
Choose 1 answer:
(A) -17.02
(B) -10.73
(c) -4.45
(D) 1.83

The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is $-0$ . $26$ . $\newline$ Which is the principal value of $\cos ^{-1}(-0.26) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $-17$ . $02$ $\newline$ (B) $-10$ . $73$ $\newline$ (C) $-4$ . $45$ $\newline$ (D) $1$ . $83$

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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 cosine is

-0

.

26

.

\newline

Which is the principal value of

\cos ^{-1}(-0.26) ?

\newline

Choose

1

answer:

\newline

(A)

-17

.

02

\newline

(B)

-10

.

73

\newline

(C)

-4

.

45

\newline

(D)

1

.

83

Principal value of inverse cosine function: The principal value of the inverse cosine function, $\cos^{-1}(x)$ , is the angle in radians between $0$ and $\pi$ for $x$ in the range $[-1, 1]$ . Since $-0.26$ is within this range, we will find an angle between $0$ and $\pi$ .
Finding the principal value: To find the principal value of $\cos^{-1}(-0.26)$ , we can use a calculator or a mathematical software that can compute inverse trigonometric functions.
Using a calculator to compute the value: Using a calculator, we find that $\cos^{-1}(-0.26) \approx 1.83$ radians when rounded to the nearest hundredth.
Determining the correct answer: The principal value of $\cos^{-1}(-0.26)$ must be a positive angle between $0$ and $\pi$ , so the correct answer is (D) $1.83$ . The other options are negative or not within the range of the principal value for the cosine inverse.

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