Which of the following radian measures is equal to $315^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5 \pi}{4}$ radians $\newline$ B $\frac{7 \pi}{4}$ radians $\newline$ (C) $\frac{9 \pi}{4}$ radians $\newline$ (D) $\frac{11 \pi}{4}$ radians

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Algebra 2

Convert between radians and degrees

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Q. Which of the following radian measures is equal to

315^{\circ}

\newline

Choose

1

answer:

\newline

(A)

\frac{5 \pi}{4}

radians

\newline

\frac{7 \pi}{4}

radians

\newline

(C)

\frac{9 \pi}{4}

radians

\newline

(D)

\frac{11 \pi}{4}

radians

Identify formula for conversion: Identify the formula to convert degrees to radians. The formula is $\text{radians} = \text{degrees} \times \left(\frac{\pi}{180^\circ}\right)$ .
Convert $315$ degrees to radians: Convert $315$ degrees into radians using the formula. By substituting $315$ degrees into the formula, we get $315^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{315}{180}\right) \times \pi = \left(\frac{7}{4}\right) \times \pi$ radians.
Simplify fraction $(\frac{315}{180}):</b> Simplify the fraction \$(\frac{315}{180})$ to its lowest terms. Dividing both the numerator and the denominator by $45$ , we get $(\frac{7}{4})$ .
Choose correct option for $315$ degrees: Choose the correct option of radians for $315$ degrees. The correct option is $(\frac{7}{4}) \times \pi$ radians, which is equivalent to $315$ degrees.

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Which of the following radian measures is equal to 315∘ 315^{\circ} 315∘ ?\newlineChoose 111 answer:\newline(A) 5π4 \frac{5 \pi}{4} 45π​ radians\newlineB 7π4 \frac{7 \pi}{4} 47π​ radians\newline(C) 9π4 \frac{9 \pi}{4} 49π​ radians\newline(D) 11π4 \frac{11 \pi}{4} 411π​ radians

Which of the following radian measures is equal to $315^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5 \pi}{4}$ radians $\newline$ B $\frac{7 \pi}{4}$ radians $\newline$ (C) $\frac{9 \pi}{4}$ radians $\newline$ (D) $\frac{11 \pi}{4}$ radians