Find the following trigonometric values. Express your answers exactly. {:[cos((5pi)/(3))=◻],[sin((5pi)/(3))=◻]:}

Determine Reference Angle: Determine the reference angle for (5pi)/3 in the unit circle. The angle (5pi)/3 is more than pi but less than 2pi, which means it is in the fourth quadrant of the unit circle. The reference angle is the positive acute angle that the terminal side of (5pi)/3 makes with the x-axis. To find the reference angle, we subtract (5pi)/3 from 2pi. Reference angle = 2pi - (5pi)/3 = (6pi - 5pi)/3 = pi/3Find Cosine: Find the cosine of the reference angle. The cosine of pi/3 is known from the unit circle to be 1/2. Since (5pi)/3 is in the fourth quadrant and the cosine is positive in the fourth quadrant, the cosine of (5pi)/3 is also 1/2. cos((5pi)/3) = cos(pi/3) = 1/2Find Sine: Find the sine of the reference angle. The sine of pi/3 is known from the unit circle to be √3/2. However, since (5pi)/3 is in the fourth quadrant and the sine is negative in the fourth quadrant, the sine of (5pi)/3 is the negative of the sine of the reference angle. sin((5pi)/3) = -sin(pi/3) = -√3/2

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Find the following trigonometric values.
Express your answers exactly.

{:[cos((5pi)/(3))=◻],[sin((5pi)/(3))=◻]:}

Find the following trigonometric values. $\newline$ Express your answers exactly. $\newline$ $\begin{array}{l} \cos \left(\frac{5 \pi}{3}\right)=\square \\ \sin \left(\frac{5 \pi}{3}\right)=\square \end{array}$

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Q. Find the following trigonometric values.

\newline

Express your answers exactly.

\newline

\begin{array}{l} \cos \left(\frac{5 \pi}{3}\right)=\square \\ \sin \left(\frac{5 \pi}{3}\right)=\square \end{array}

Determine Reference Angle: Determine the reference angle for $(5\pi)/3$ in the unit circle. $\newline$ The angle $(5\pi)/3$ is more than $\pi$ but less than $2\pi$ , which means it is in the fourth quadrant of the unit circle. The reference angle is the positive acute angle that the terminal side of $(5\pi)/3$ makes with the x-axis. To find the reference angle, we subtract $(5\pi)/3$ from $2\pi$ . $\newline$ Reference angle = $2\pi - (5\pi)/3 = (6\pi - 5\pi)/3 = \pi/3$
Find Cosine: Find the cosine of the reference angle. $\newline$ The cosine of $\pi/3$ is known from the unit circle to be $1/2$ . Since $(5\pi)/3$ is in the fourth quadrant and the cosine is positive in the fourth quadrant, the cosine of $(5\pi)/3$ is also $1/2$ . $\newline$ $\cos((5\pi)/3) = \cos(\pi/3) = 1/2$
Find Sine: Find the sine of the reference angle. $\newline$ The sine of $\pi/3$ is known from the unit circle to be $\sqrt{3}/2$ . However, since $(5\pi)/3$ is in the fourth quadrant and the sine is negative in the fourth quadrant, the sine of $(5\pi)/3$ is the negative of the sine of the reference angle. $\newline$ $\sin((5\pi)/3) = -\sin(\pi/3) = -\sqrt{3}/2$