Which of the following radian measures is equal to 75^(@) ? Choose 1 answer: (A) (pi)/(12) radians (B) (pi)/(3) radians (C) (5pi)/(12) radians (D) (7pi)/(12) radians

Identify Formula: Identify the formula to convert degrees to radians. The formula is radians = degrees * (π/180°).Convert Degrees to Radians: Convert 75 degrees to radians using the formula. By substituting 75 degrees into the formula, we get 75° * (π/180°) = (75/180) * π = (5/12) * π radians.Simplify Fraction: Simplify the fraction (5/12) * π to find the radian measure. The fraction is already in its simplest form, so the radian measure is (5π/12) radians.Choose Correct Option: Choose the correct option of radians for 75 degrees. The correct option is (5π/12) radians, which is equivalent to 75 degrees.

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Which of the following radian measures is equal to
75^(@) ?
Choose 1 answer:
(A)
(pi)/(12) radians
(B)
(pi)/(3) radians
(C)
(5pi)/(12) radians
(D)
(7pi)/(12) radians

Which of the following radian measures is equal to $75^{\circ}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{\pi}{12}$ radians $\newline$ (B) $\frac{\pi}{3}$ radians $\newline$ (C) $\frac{5\pi}{12}$ radians $\newline$ (D) $\frac{7\pi}{12}$ radians

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Math Problems

Algebra 2

Convert between radians and degrees

Full solution

Q. Which of the following radian measures is equal to

75^{\circ}

\newline

Choose

1

answer:

\newline

(A)

\frac{\pi}{12}

radians

\newline

(B)

\frac{\pi}{3}

radians

\newline

(C)

\frac{5\pi}{12}

radians

\newline

(D)

\frac{7\pi}{12}

radians

Identify Formula: Identify the formula to convert degrees to radians. The formula is $\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right)$ .
Convert Degrees to Radians: Convert $75$ degrees to radians using the formula. By substituting $75$ degrees into the formula, we get $75^\circ \times (\pi/180^\circ) = (75/180) \times \pi = (5/12) \times \pi$ radians.
Simplify Fraction: Simplify the fraction $(\frac{5}{12}) \cdot \pi$ to find the radian measure. The fraction is already in its simplest form, so the radian measure is $(\frac{5\pi}{12})$ radians.
Choose Correct Option: Choose the correct option of radians for $75$ degrees. The correct option is $\frac{5\pi}{12}$ radians, which is equivalent to $75$ degrees.