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Trig Relationships and the Pythagorean Theorem

Know and use the relationship

(1) $\begin{equation*} sin^{2}(x) + cos^{2}(x) = 1\end{equation*}$

(2) $\begin{equation*} sin(A) = \frac{3}{5}\quad cos(A) = \frac{4}{5}\end{equation*}$

(3) $\begin{equation*} a^{2} + b^{2} = c^{2} \end{equation*}$

(4) $\begin{equation*} 3^{2} + 4^{2} = 5^{2}\end{equation*}$

(5) $\begin{equation*} 9 + 16 = 25 \end{equation*}$

(6) $\begin{equation*} 25 = 25 \checkmark \end{equation*}$

(7) $\begin{equation*}(\frac{3}{5})^{2} + (\frac{4}{5}^{2} = 1 \end{equation*}$

(8) $\begin{equation*}(\frac{3^2}{5^2}) + (\frac{4^2}{5^2}) = 1 \end{equation*}$

(9) $\begin{equation*} \frac{9}{25} + \frac{16}{25} = 1 \end{equation*}$

(10) $\begin{equation*} 1 = 1 \checkmark \end{equation*}$

(11) $\begin{equation*} sin(A) = \frac{a}{c}\quad cos(A) = \frac{b}{c} \end{equation*}$

(12) $\begin{equation*} \frac{a^{2} + b^{2}}{c^{2}} = \frac{c^{2}}{c^{2}}\end{equation*}$

(13) $\begin{equation*} \frac{a^{2}}{c^{2}} + \frac{b^{2}}{c^{2}}= 1 \end{equation*}$

(14) $\begin{equation*} (\frac{a}{c})^{2} + (\frac{b}{c})^{2} = 1 \end{equation*}$

(15) $\begin{equation*} (sin(A))^2 + (cos(A))^{2} = 1 \end{equation*}$