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The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is 0.32 .
Which is the principal value of
cos^(-1)(0.32) ?
Choose 1 answer:
(A) -5.04
(B) 1.25
(C) 7.53
(D) 13.81

The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is $0$ . $32$ . $\newline$ Which is the principal value of $\cos ^{-1}(0.32)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-5$ . $04$ $\newline$ (B) $1$ . $25$ $\newline$ (C) $7$ . $53$ $\newline$ (D) $13$ . $81$

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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

.

32

.

\newline

Which is the principal value of

\cos ^{-1}(0.32)

?

\newline

Choose

1

answer:

\newline

(A)

-5

.

04

\newline

(B)

1

.

25

\newline

(C)

7

.

53

\newline

(D)

13

.

81

Definition 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 which the cosine is $x$ . Since $0.32$ is positive, the principal value will be in the first quadrant.
Determine Principal Value: To find the principal value of $\cos^{-1}(0.32)$ , we can use a calculator or a computer to compute the inverse cosine of $0.32$ .
Calculate Inverse Cosine: Using a calculator, we find that $\cos^{-1}(0.32) \approx 1.241$ radians when rounded to the nearest hundredth.
Identify Closest Value: Looking at the options provided, the value that is closest to $1.241$ radians and falls within the range of $0$ to $\pi$ is $1.25$ radians. Therefore, the principal value of $\cos^{-1}(0.32)$ is (B) $1.25$ .

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