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The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is -0.65 .
Which is the principal value of
arccos(-0.65)?
Choose 1 answer:
(A) -10.29
(B) -4.00
(C)
2.28
(D) 8.56

The following are all angle measures (in radians, rounded to the nearest hundredth) whose cosine is $-0$ . $65$ . $\newline$ Which is the principal value of $\arccos (-0.65) ?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\quad-10.29$ $\newline$ (B) $-4$ . $00$ $\newline$ (C) $\mathbf{2 . 2 8}$ $\newline$ (D) $8$ . $56$

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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

.

65

.

\newline

Which is the principal value of

\arccos (-0.65) ?

\newline

Choose

1

answer:

\newline

(A)

\quad-10.29

\newline

(B)

-4

.

00

\newline

(C)

\mathbf{2 . 2 8}

\newline

(D)

8

.

56

Identify Quadrant: The principal value of $\arccos(x)$ is the unique value $y$ in the range $[0, \pi]$ such that $\cos(y) = x$ . Since $-0.65$ is negative, the principal value must be in the second quadrant where cosine is negative.
Find Angle: To find the principal value of $\arccos(-0.65)$ , we use a calculator or a trigonometric table to find the angle whose cosine is $-0.65$ . Remember that the principal value will be in the range $[0, \pi]$ .
Calculate Value: Using a calculator, we find that $\arccos(-0.65) \approx 2.28$ radians. This is the angle in the second quadrant and falls within the principal range $[0, \pi]$ .
Select Correct Option: Looking at the options provided, (C) $2.28$ is the only value that is positive and falls within the range $[0, \pi]$ . Therefore, this must be the principal value of $\arccos(-0.65)$ .

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