6.2 Trigonometric Functions: Unit Circle Approach/78

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta \rightarrow (5, -12)}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta \rightarrow x=5, \, y=-12, \, r=\,? }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} (5)^2+(-12)^2 &= r^2 \\ 25+144 &= r^2 \\ 169 &= r^2 \\ \sqrt{169} &= \sqrt{r^2}\\ 13 &= r \\ \end{align} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \theta \rightarrow x=5, \, y=-12, \, r=13 }

${\begin{aligned}\sin {(\theta )}&={\frac {-12}{13}}&\csc {(\theta )}&={\frac {13}{-12}}\\[2ex]\cos {(\theta )}&={\frac {5}{13}}&\sec {(\theta )}&={\frac {13}{5}}\\[2ex]\tan {(\theta )}&={\frac {-12}{5}}&\cot {(\theta )}&={\frac {5}{-12}}\\[2ex]\end{aligned}}$