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Apuntes

``` Function Relationships sin θ = \frac{1}{\csc θ} csc θ = \frac{1}{\sin θ} cos θ = \frac{1}{\sec θ} sec θ = \frac{1}{\cos θ} tan θ = \frac{1}{\cot θ} cot θ = \frac{1}{\tan θ} Opposite Angle Formulas sin (-θ) = -\sin (θ) cos (-θ) = \cos (θ) tan (-θ) = -\tan (θ) cot (-θ) = -\cot (θ) sec (-θ) = \sec (θ) csc (-θ) = -\csc (θ) Cofunction Formulas (in Quadrant I) sin θ = \cos \left(\frac{π}{2} - θ\right) cos θ = \sin \left(\frac{π}{2} - θ\right) tan θ = \cot \left(\frac{π}{2} - θ\right) cot θ = \tan \left(\frac{π}{2} - θ\right) sec θ = \csc \left(\frac{π}{2} - θ\right) csc θ = \sec \left(\frac{π}{2} - θ\right) Pythagorean Identities \sin^2 θ + \cos^2 θ = 1 \tan^2 θ + 1 = \sec^2 θ \cot^2 θ + 1 = \csc^2 θ Half Angle Formulas \sin \frac{θ}{2} = ± \sqrt{\frac{1 - \cos θ}{2}} \cos \frac{θ}{2} = ± \sqrt{\frac{1 + \cos θ}{2}} \tan \frac{θ}{2} = ± \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = \frac{1 - \cos θ}{\sin θ} = \frac{\sin θ}{1 + \cos θ} Angle Addition Formulas \sin (A + B) = \sin A \cos B + \cos A \sin B \sin (A - B) = \sin A \cos B - \cos A \sin B \cos (A + B) = \cos A \cos B - \sin A \sin B \cos (A - B) = \cos A \cos B + \sin A \sin B \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \t...