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Reciprocal Identities

\[ \begin{align*} {\color{flatlightblue}\csc(\theta)} &= \dfrac{1}{\color{flatblue}\sin(\theta)} & {\color{flatlightred}\sec(\theta)} &= \dfrac{1}{\color{flatred}\cos(\theta)} & {\color{flatlightgreen}\cot(\theta)} &= \dfrac{1}{\color{flatgreen}\tan(\theta)} \\ {\color{flatblue}\sin(\theta)} &= \dfrac{1}{\color{flatlightblue}\csc(\theta)} & {\color{flatred}\cos(\theta)} &= \dfrac{1}{\color{flatlightred}\sec(\theta)} & {\color{flatgreen}\tan(\theta)} &= \dfrac{1}{\color{flatlightgreen}\cot(\theta)} \end{align*} \]

Quotient Identities

\[ \begin{align*} {\color{flatgreen}\tan(\theta)} &= \dfrac{\color{flatblue}\sin(\theta)}{\color{flatred}\cos(\theta)} & {\color{flatlightgreen}\cot(\theta)} &= \dfrac{\color{flatred}\cos(\theta)}{\color{flatblue}\sin(\theta)} & \end{align*} \]

Pythagorean Identities

\[ \begin{align*} {\color{flatblue}\sin^2(\theta)}+{\color{flatred}\cos^2(\theta)} &= {1} \\ {\color{flatgreen}\tan^2(\theta)}\ \ \ +\ \ \ {1}\ \ \ &= {\color{flatlightred}\sec^2(\theta)} \\ {1}\ \ \ +\ \ \ {\color{flatlightgreen}\cot^2(\theta)} &= {\color{flatlightblue}\csc^2(\theta)} \end{align*} \]

Cofunction Identities

\[ \begin{align*} {\sin({\color{flatpurple}\theta})} &= {\cos({\color{flatpink}\tfrac\pi2-\theta})} & {\tan({\color{flatpurple}\theta})} &= {\cot({\color{flatpink}\tfrac\pi2-\theta})} & {\sec({\color{flatpurple}\theta})} &= {\csc({\color{flatpink}\tfrac\pi2-\theta})} \\ {\cos({\color{flatpurple}\theta})} &= {\sin({\color{flatpink}\tfrac\pi2-\theta})} & {\cot({\color{flatpurple}\theta})} &= {\tan({\color{flatpink}\tfrac\pi2-\theta})} & {\csc({\color{flatpurple}\theta})} &= {\sec({\color{flatpink}\tfrac\pi2-\theta})} \end{align*} \]

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