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 for radians to degrees: To convert radians to degrees, we use the conversion factor that π radians is equal to 180 degrees. Therefore, we multiply the given radian measure by 180/π to convert it to degrees. Calculation: θ in degrees = θ in radians × (180/π) θ in degrees = (4π/9) × (180/π)Calculation of θ in degrees: Now, we simplify the expression by canceling out the π in the numerator and the denominator. Calculation: θ in degrees = (4/9) × 180Simplification of the expression: Next, we multiply 4 by 180 and then divide by 9 to find the value of θ in degrees. Calculation: θ in degrees = (4 × 180) / 9 θ in degrees = 720 / 9Calculation of θ in degrees: Finally, we perform the division to get the value of θ. Calculation: θ in degrees = 720 / 9 θ in degrees = 80

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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

Inverses of sin, cos, and tan: degrees

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 for radians to degrees: To convert radians to degrees, we use the conversion factor that $\pi$ radians is equal to $180$ degrees. Therefore, we multiply the given radian measure by $\frac{180}{\pi}$ to convert it to degrees. $\newline$ Calculation: $\theta$ in degrees = $\theta$ in radians $\times \left(\frac{180}{\pi}\right)$ $\newline$ $\theta$ in degrees = $\left(\frac{4\pi}{9}\right) \times \left(\frac{180}{\pi}\right)$
Calculation of $\theta$ in degrees: Now, we simplify the expression by canceling out the $\pi$ in the numerator and the denominator. $\newline$ Calculation: $\theta$ in degrees = $\left(\frac{4}{9}\right) \times 180$
Simplification of the expression: Next, we multiply $4$ by $180$ and then divide by $9$ to find the value of $\theta$ in degrees. $\newline$ Calculation: $\theta$ in degrees = $(4 \times 180) / 9$ $\newline$ $\theta$ in degrees = $720 / 9$
Calculation of $\theta$ in degrees: Finally, we perform the division to get the value of $\theta$ . $\newline$ Calculation: $\theta$ in degrees = $\frac{720}{9}$ $\newline$ $\theta$ in degrees = $80$