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The following are all angle measures, in degrees, whose cosine is -1 .
Which is the principal value of
arccos(-1) ?
Choose 1 answer:
(A)
-540^(@)
(B)
-180^(@)
(c)
180^(@)
(D)
540^(@)

The following are all angle measures, in degrees, whose cosine is $-1$ . $\newline$ Which is the principal value of $\arccos (-1)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-540^{\circ}$ $\newline$ (B) $-180^{\circ}$ $\newline$ (C) $180^{\circ}$ $\newline$ (D) $540^{\circ}$

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Inverses of csc, sec, and cot

Full solution

Q. The following are all angle measures, in degrees, whose cosine is

-1

.

\newline

Which is the principal value of

\arccos (-1)

?

\newline

Choose

1

answer:

\newline

(A)

-540^{\circ}

\newline

(B)

-180^{\circ}

\newline

(C)

180^{\circ}

\newline

(D)

540^{\circ}

Identify principal value range: Identify the principal value range for arccosine function. $\newline$ The principal value for arccosine, or the inverse cosine function, is between $0$ and $180$ degrees.
Determine angle with cosine $-1$ : Determine the angle whose cosine is $-1$ within the principal value range. $\newline$ The cosine of $180$ degrees is $-1$ , which is within the principal value range for arccosine.
Eliminate options not within range: Eliminate the options that are not within the principal value range. Options (A) $-540$ degrees and (D) $540$ degrees are not within the principal value range of $0$ to $180$ degrees. Option (B) $-180$ degrees is also not within the principal value range. Therefore, these options are incorrect.
Choose correct answer: Choose the correct answer from the remaining options. $\newline$ The only option left that is within the principal value range and whose cosine is $-1$ is (C) $180$ degrees.

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