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Which of the following radian measures is equal to
90^(@) ?
Choose 1 answer:
A)
(pi)/(3) radians
(B)
(pi)/(4) radians
(C)
(pi)/(2) radians
(D)
(pi)/(6) radians

Which of the following radian measures is equal to $90^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\pi}{3}$ radians $\newline$ B $\frac{\pi}{4}$ radians $\newline$ (C) $\frac{\pi}{2}$ radians $\newline$ (D) $\frac{\pi}{6}$ radians

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Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

90^{\circ}

?

\newline

Choose

1

answer:

\newline

(A)

\frac{\pi}{3}

radians

\newline

B

\frac{\pi}{4}

radians

\newline

(C)

\frac{\pi}{2}

radians

\newline

(D)

\frac{\pi}{6}

radians

Set up proportion: To convert degrees to radians, we use the conversion factor that $180$ degrees is equal to $\pi$ radians. Therefore, to find the radian measure equivalent to $90$ degrees, we set up the proportion: $(90 \text{ degrees}) \times (\pi \text{ radians} / 180 \text{ degrees})$ .
Simplify proportion: Simplify the proportion by dividing both the numerator and the denominator by $90$ : $(\frac{90}{90}) \times (\frac{\pi}{180/90}) = 1 \times (\frac{\pi}{2}) = \frac{\pi}{2}$ radians.
Compare with options: Now we compare the result with the given options to find the correct one. $\pi/2$ radians is the same as option $(C)$ .

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\newline

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\newline

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