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

Consider Range of Cosine Inverse: To find the principal value of the inverse cosine function, we need to consider the range of the principal values for the cosine inverse, which is from 0 to π for positive values and from -π to 0 for negative values. Since -0.26 is a negative value, we are looking for an angle in the third or fourth quadrant where the cosine is negative. Identify Quadrant for Principal Value: The principal value of cos^(-1)(-0.26) will be in the second quadrant because cosine is negative there, and the range of the inverse cosine function for negative values is from 0 to π. Use Calculator for Computation: To find the principal value, we can use a calculator to compute cos^(-1)(-0.26). Make sure the calculator is set to radian mode since the answers are given in radians. Calculate Principal Value: Using a calculator, we find that cos^(-1)(-0.26) ≈ 1.83 radians. Verify within Range: Since 1.83 radians is within the range of 0 to π, it is the principal value for cos^(-1)(-0.26). Therefore, the correct answer is (D) 1.83.

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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 $\mathbf{- 0 . 2 6}$ . $\newline$ 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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Q. The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is

\mathbf{- 0 . 2 6}

\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

Consider Range of Cosine Inverse: To find the principal value of the inverse cosine function, we need to consider the range of the principal values for the cosine inverse, which is from $0$ to $\pi$ for positive values and from $-\pi$ to $0$ for negative values. Since $-0.26$ is a negative value, we are looking for an angle in the third or fourth quadrant where the cosine is negative.
Identify Quadrant for Principal Value: The principal value of $\cos^{-1}(-0.26)$ will be in the second quadrant because cosine is negative there, and the range of the inverse cosine function for negative values is from $0$ to $\pi$ .
Use Calculator for Computation: To find the principal value, we can use a calculator to compute $\cos^{-1}(-0.26)$ . Make sure the calculator is set to radian mode since the answers are given in radians.
Calculate Principal Value: Using a calculator, we find that $\cos^{-1}(-0.26) \approx 1.83$ radians.
Verify within Range: Since $1.83$ radians is within the range of $0$ to $\pi$ , it is the principal value for $\cos^{-1}(-0.26)$ . Therefore, the correct answer is (D) $1.83$ .