Find the following trigonometric values. Express your answers exactly. {:[cos((7pi)/(4))=],[sin((7pi)/(4))=]:}

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Find the following trigonometric values. Express your answers exactly.  {:[cos((7pi)/(4))=],[sin((7pi)/(4))=]:}

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Understand the unit circle: Understand the unit circle and the values of cosine and sine for special angles. The unit circle allows us to find the values of sine and cosine for multiples of π/4, π/2, π, and so on. The angles (7π/4) and (π/4) are coterminal, meaning they share the same terminal side on the unit circle. Therefore, cos((7π/4)) and sin((7π/4)) will have the same absolute values as cos((π/4)) and sin((π/4)), but possibly different signs depending on the quadrant in which the angle (7π/4) lies.Determine the quadrant: Determine the quadrant in which the angle (7π/4) lies. The angle (7π/4) is more than 2π but less than 2π + π/4, which means it is in the fourth quadrant of the unit circle. In the fourth quadrant, cosine is positive and sine is negative.Calculate cos((7π/4)): Calculate the value of cos((7π/4)). Since (7π/4) is coterminal with (π/4), and we know that cos((π/4)) = √2/2, we can say that cos((7π/4)) = √2/2 because cosine is positive in the fourth quadrant.Calculate sin((7π/4)): Calculate the value of sin((7π/4)). Similarly, since (7π/4) is coterminal with (π/4), and we know that sin((π/4)) = √2/2, we can say that sin((7π/4)) = -√2/2 because sine is negative in the fourth quadrant.

Find the following trigonometric values. $\newline$ Express your answers exactly. $\newline$ $\begin{array}{l} \cos \left(\frac{7 \pi}{4}\right)= \\ \sin \left(\frac{7 \pi}{4}\right)= \end{array}$

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Find the following trigonometric values.\newlineExpress your answers exactly.\newlinecos⁡(7π4)=sin⁡(7π4)= \begin{array}{l} \cos \left(\frac{7 \pi}{4}\right)= \\ \sin \left(\frac{7 \pi}{4}\right)= \end{array} cos(47π​)=sin(47π​)=​

Find the following trigonometric values. $\newline$ Express your answers exactly. $\newline$ $\begin{array}{l} \cos \left(\frac{7 \pi}{4}\right)= \\ \sin \left(\frac{7 \pi}{4}\right)= \end{array}$