Trigonometry Formula Sheet General Chemistry I (CHEM 1311) Amanda Campbell

Right Triangle Trigonometry sin𝜃=𝑜𝑝𝑝ℎ𝑦𝑝 csc𝜃=ℎ𝑦𝑝𝑜𝑝𝑝 cos𝜃=𝑎𝑑𝑗ℎ𝑦𝑝 sec𝜃=ℎ𝑦𝑝𝑎𝑑𝑗 tan𝜃=𝑜𝑝𝑝𝑎𝑑𝑗 cot𝜃=𝑎𝑑𝑗𝑜𝑝𝑝 Unit Circle Trigonometry sin𝜃=𝑦𝑟=𝑦1 csc𝜃=𝑟𝑦=1𝑦 cos𝜃=𝑥𝑟=𝑥1 sec𝜃=𝑟𝑥=1𝑥 tan𝜃=𝑦𝑥 cot𝜃=𝑥𝑦 Degrees to Radians (𝑥°1)×( 𝜋180°)=𝑟𝑎𝑑𝑖𝑎𝑛 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 Radians to Degrees (𝑥𝜋1)×(180°𝜋)=𝑑𝑒𝑔𝑟𝑒𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 Tangent & Cotangent Identities tan𝜃=sin𝜃cos𝜃 cot𝜃=cos𝜃sin𝜃 Reciprocal Identities sin𝜃= 1csc𝜃 csc𝜃= 1sin𝜃 cos𝜃= 1sec𝜃 sec𝜃= 1cos𝜃 tan𝜃= 1cot𝜃 cot𝜃= 1tan𝜃 Pythagorean Identities sin2𝜃+cos2𝜃=1 tan2𝜃+1=sec2𝜃 1+cot2𝜃=csc2𝜃 Cofunction Formulas sin(𝜋2−𝜃)=cos𝜃 cos(𝜋2−𝜃)=sin𝜃 csc(𝜋2−𝜃)=sec𝜃 sec(𝜋2−𝜃)=csc𝜃 tan(𝜋2−𝜃)=cot𝜃 cot(𝜋2−𝜃)=tan𝜃 Definition of Inverse Functions 𝜃=sin−1(𝑥) is equal to 𝑥=sin𝜃 𝜃=cos−1(𝑥) is equal to 𝑥=cos𝜃 𝜃=tan−1(𝑥) is equal to 𝑥=tan𝜃 Other Notations sin−1(𝑥)=arcsin(𝑥) cos−1(𝑥)=arccos(𝑥

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