If theta=(4pi)/(9) radians, what is the value of theta in degrees? Choose 1 answer: (A) 20^(@) (B) 36^(@) (C) 80^(@) (D) 720^(@)

Conversion Factor: To convert radians to degrees, we use the conversion factor that $ \pi $ radians is equal to 180 degrees. The question prompt is: ＂What is the value of $ \theta $ in degrees when $ \theta = \frac{4\pi}{9} $ radians?＂Multiply by Conversion Factor: We multiply $ \theta $ by the conversion factor $ \frac{180^\circ}{\pi} $ to convert from radians to degrees: $ \theta \times \frac{180^\circ}{\pi} = \frac{4\pi}{9} \times \frac{180^\circ}{\pi} $.Cancel out $ \pi $: The $ \pi $ in the numerator and the $ \pi $ in the denominator cancel out, leaving us with $ \frac{4}{9} \times 180^\circ $.Calculate Multiplication: We calculate the multiplication: $ \frac{4}{9} \times 180^\circ = \frac{4 \times 180^\circ}{9} $.Final Result: Divide 180 by 9 to get 20, and then multiply by 4: $ 20 \times 4 = 80^\circ $.

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If
theta=(4pi)/(9) radians, what is the value of
theta in degrees?
Choose 1 answer:
(A)
20^(@)
(B)
36^(@)
(C)
80^(@)
(D)
720^(@)

If $\theta=\frac{4\pi}{9}$ radians, what is the value of $\theta$ in degrees? $\newline$ Choose $1$ answer: $\newline$ (A) $20^{\circ}$ $\newline$ (B) $36^{\circ}$ $\newline$ (C) $80^{\circ}$ $\newline$ (D) $720^{\circ}$

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Math Problems

Algebra 2

Simplify expressions using trigonometric identities

Full solution

Q. If

\theta=\frac{4\pi}{9}

radians, what is the value of

\theta

in degrees?

\newline

Choose

1

answer:

\newline

(A)

20^{\circ}

\newline

(B)

36^{\circ}

\newline

(C)

80^{\circ}

\newline

(D)

720^{\circ}

Conversion Factor: To convert radians to degrees, we use the conversion factor that $\pi$ radians is equal to $180$ degrees. The question prompt is: ＂What is the value of $\theta$ in degrees when $\theta = \frac{4\pi}{9}$ radians?＂
Multiply by Conversion Factor: We multiply $\theta$ by the conversion factor $\frac{180^\circ}{\pi}$ to convert from radians to degrees: $\theta \times \frac{180^\circ}{\pi} = \frac{4\pi}{9} \times \frac{180^\circ}{\pi}$ .
Cancel out $\pi$ : The $\pi$ in the numerator and the $\pi$ in the denominator cancel out, leaving us with $\frac{4}{9} \times 180^\circ$ .
Calculate Multiplication: We calculate the multiplication: $\frac{4}{9} \times 180^\circ = \frac{4 \times 180^\circ}{9}$ .
Final Result: Divide $180$ by $9$ to get $20$ , and then multiply by $4$ : $20 \times 4 = 80^\circ$ .