Trigonometry formula sheet, Cheat Sheet of Trigonometry

Download Trigonometry formula sheet and more Cheat Sheet Trigonometry in PDF only on Docsity! Updated: October 2019 Reciprocal Identities: sin𝜃𝜃 = 1 csc 𝜃𝜃 csc𝜃𝜃 = 1 sin 𝜃𝜃 cos𝜃𝜃 = 1 sec 𝜃𝜃 sec 𝜃𝜃 = 1 cos 𝜃𝜃 tan 𝜃𝜃 = 1 cot𝜃𝜃 cot𝜃𝜃 = 1 tan𝜃𝜃 Trigonometry Formulas and Properties Tangent and Cotangent Identities: tan 𝜃𝜃 = sin 𝜃𝜃 cos𝜃𝜃 cot = cos 𝜃𝜃 sin𝜃𝜃 Pythagorean Identities: sin2 𝜃𝜃 + cos2 𝜃𝜃 = 1 tan2 𝜃𝜃 + 1 = sec2 𝜃𝜃 1 + cot2 𝜃𝜃 = csc2 𝜃𝜃 Even/Odd Formulas: sin(−𝜃𝜃) = − sin𝜃𝜃 cos(−𝜃𝜃) = cos𝜃𝜃 tan(−𝜃𝜃) = − tan 𝜃𝜃 csc(−𝜃𝜃) = − csc 𝜃𝜃 sec(−𝜃𝜃) = sec𝜃𝜃 cot(−𝜃𝜃) = − cot𝜃𝜃 Cofunction Formulas: sin � 𝜋𝜋 2 − 𝜃𝜃� = cos 𝜃𝜃 csc � 𝜋𝜋 2 − 𝜃𝜃� = sec 𝜃𝜃 tan � 𝜋𝜋 2 − 𝜃𝜃� = cot𝜃𝜃 cos � 𝜋𝜋 2 − 𝜃𝜃� = sin 𝜃𝜃 sec � 𝜋𝜋 2 − 𝜃𝜃� = csc 𝜃𝜃 cot � 𝜋𝜋 2 − 𝜃𝜃� = tan𝜃𝜃 Product to Sum Formulas: sin𝛼𝛼 sin𝛽𝛽 = 1 2 [cos(𝛼𝛼 − 𝛽𝛽) − cos(𝛼𝛼 + 𝛽𝛽)] cos𝛼𝛼 cos𝛽𝛽 = 1 2 [cos(𝛼𝛼 − 𝛽𝛽) + cos(𝛼𝛼 + 𝛽𝛽)] sin𝛼𝛼 cos𝛽𝛽 = 1 2 [sin(𝛼𝛼 + 𝛽𝛽) + sin(𝛼𝛼 − 𝛽𝛽)] cos𝛼𝛼 sin𝛽𝛽 = 1 2 [sin(𝛼𝛼 + 𝛽𝛽) − sin(𝛼𝛼 − 𝛽𝛽)] Sum to Product Formulas: sin𝛼𝛼 + sin𝛽𝛽 = 2 sin � 𝛼𝛼 + 𝛽𝛽 2 � cos � 𝛼𝛼 − 𝛽𝛽 2 � sin𝛼𝛼 − sin𝛽𝛽 = 2 cos � 𝛼𝛼 + 𝛽𝛽 2 � sin � 𝛼𝛼 − 𝛽𝛽 2 � cos𝛼𝛼 + cos𝛽𝛽 = 2 cos � 𝛼𝛼 + 𝛽𝛽 2 � cos � 𝛼𝛼 − 𝛽𝛽 2 � cos𝛼𝛼 − cos𝛽𝛽 = −2 sin � 𝛼𝛼 + 𝛽𝛽 2 � sin � 𝛼𝛼 − 𝛽𝛽 2 � Sum and Difference Formulas: sin(𝛼𝛼 ± 𝛽𝛽) = sin𝛼𝛼 cos𝛽𝛽 ± sin𝛽𝛽 cos𝛼𝛼 cos(𝛼𝛼 ± 𝛽𝛽) = cos𝛼𝛼 cos𝛽𝛽 ∓ sin𝛼𝛼 sin𝛽𝛽 tan(𝛼𝛼 ± 𝛽𝛽) = tan𝛼𝛼 ± tan𝛽𝛽 1 ∓ tan𝛼𝛼 tan𝛽𝛽 Periodic Formulas: sin(𝜃𝜃 + 2𝜋𝜋𝜋𝜋) = sin𝜃𝜃 csc(𝜃𝜃 + 2𝜋𝜋𝜋𝜋) = csc 𝜃𝜃 cos(𝜃𝜃 + 2𝜋𝜋𝜋𝜋) = cos𝜃𝜃 sec(𝜃𝜃 + 2𝜋𝜋𝜋𝜋) = sec𝜃𝜃 tan(𝜃𝜃 + 𝜋𝜋𝜋𝜋) = tan𝜃𝜃 cot(𝜃𝜃 + 𝜋𝜋𝜋𝜋) = cot𝜃𝜃 Half-Angle Formulas: sin � 𝜃𝜃 2� = ±� 1 − cos𝜃𝜃 2 cos � 𝜃𝜃 2� = ±� 1 + cos 𝜃𝜃 2 tan � 𝜃𝜃 2� = ±� 1 − cos 𝜃𝜃 1 + cos 𝜃𝜃 Double Angle Formulas: sin(2𝜃𝜃) = 2 sin 𝜃𝜃 cos 𝜃𝜃 cos(2𝜃𝜃) = cos2 𝜃𝜃 −sin2 𝜃𝜃 = 2 cos2 𝜃𝜃 − 1 = 1 − 2 sin2 𝜃𝜃 tan 2𝜃𝜃 = 2tan𝜃𝜃 1 − tan2 𝜃𝜃