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Complete this input/output chart. Write the rule for finding
y.

x

y

10
6

8
5

6

3

y=

$14$ . Complete this input/output chart. Write the rule for finding $y$ . $\newline$ \begin{tabular}{|c|c|} $\newline$ \hline $x$ & $y$ \\ $\newline$ \hline $10$ & $6$ \\ $\newline$ \hline $8$ & $5$ \\ $\newline$ \hline $6$ & \\ $\newline$ \hline & $3$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ $y=$

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Find trigonometric ratios using reference angles

Full solution

Q.

14

. Complete this input/output chart. Write the rule for finding

y

.

\newline

\begin{tabular}{|c|c|}

\newline

\hline

x

&

y

\\

\newline

\hline

10

&

6

\\

\newline

\hline

8

&

5

\\

\newline

\hline

6

& \\

\newline

\hline &

3

\\

\newline

\hline

\newline

\end{tabular}

\newline

y=

Observe $x$ and $y$ values: Look at the differences between the $x$ values and their corresponding $y$ values. The $x$ values decrease by $2$ each time, let's see if there's a pattern with the $y$ values.
Identify pattern in values: When $x$ decreases by $2$ (from $10$ to $8$ ), $y$ decreases by $1$ (from $6$ to $5$ ). Let's assume this pattern continues and apply it to find $y$ when $x$ is $6$ .
Apply pattern to find $y$ : If we subtract $1$ from $y$ when $x$ is $8$ (which is $5$ ), we get $y = 4$ for $x = 6$ .
Calculate $y$ for $x=3$ : Now, let's find $y$ when $x$ is $3$ . We need to subtract $3$ from $x=6$ to get $x=3$ , so we should subtract $1.5$ from $y=4$ (since $y$ changes by $x=3$ $1$ for every $x=3$ $2$ change in $x$ ).

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