Find the reference angle for a rotation of (5pi)/(9). Answer:

Identify Range: Identify the range of the given angle. Since (5π)/(9) radians is greater than π/2 but less than π, it lies in the second quadrant.Concept of Reference Angle: Understand the concept of a reference angle. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For angles in the second quadrant, the reference angle is π minus the given angle.Calculate Reference Angle: Calculate the reference angle. Reference angle = π - (5π)/(9) = (9π)/(9) - (5π)/(9) = (4π)/(9)Check Result: Check the result. Since (4π)/(9) is less than π/2, it is an acute angle, which is appropriate for a reference angle.

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Find the reference angle for a rotation of
(5pi)/(9).
Answer:

Find the reference angle for a rotation of $\frac{5 \pi}{9}$ . $\newline$ Answer: $\newline$

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Math Problems

Algebra 2

Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{5 \pi}{9}

\newline

Answer:

\newline

Identify Range: Identify the range of the given angle. $\newline$ Since $(5\pi)/(9)$ radians is greater than $\pi/2$ but less than $\pi$ , it lies in the second quadrant.
Concept of Reference Angle: Understand the concept of a reference angle. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For angles in the second quadrant, the reference angle is $\pi$ minus the given angle.
Calculate Reference Angle: Calculate the reference angle. $\newline$ Reference angle = $\pi - \frac{5\pi}{9}$ $\newline$ = $\frac{9\pi}{9} - \frac{5\pi}{9}$ $\newline$ = $\frac{4\pi}{9}$
Check Result: Check the result. $\newline$ Since $(\frac{4\pi}{9})$ is less than $\frac{\pi}{2}$ , it is an acute angle, which is appropriate for a reference angle.