#Maths Trigonometric identities are pretty far down on my bucket list of things to learn, but they're important regardless! This is **especially** true if you take additional mathematics, so make sure the base identities here are commuted to memory! [[#Derivations]] for reference and questions. # Trig Identities Basic $\cos^2 \theta + \sin^2 \theta = 1$ $\csc \theta = \frac{1}{\sin \theta}$ $\sec\theta = \frac{1}{\cos \theta}$ $\cot \theta = \frac{1}{\tan \theta}$ ## Double Angle Identities $\cos{2}\theta = \cos^2\theta-\sin^2\theta$ $\cos2\theta = 1-2\sin^2\theta$ $\cos 2\theta = 2\cos^2\theta-1$ $\sin{2}\theta = 2\sin \theta \cos \theta$ $\tan 2\theta = \frac{2\tan\theta}{1-\tan^2 \theta}$ ## Compound Angle Identities $\sin(A+B) = \sin A\cos B + \cos A\sin B$ $\sin(A-B) = \sin A\cos B-\cos B\sin A$ $\cos(A+B) = \cos A\cos B -\sin A\sin B$ $\cos(A-B) = \cos A\cos B + \sin A\sin B$ $\tan(A+B) = \frac{{\tan A + \tan B}}{1-\tan A\tan B}$ $\tan(A-B) = \frac{{\tan A - \tan B}}{1+\tan A\tan B}$ ## Half Angle Identities - TBD usefulness # The Stupid ## Inverse Trig Identities $\tan^2\theta + 1 = sec^2\theta$ $\cot^2\theta + 1 = \csc^2\theta$ ## Complex Trig Identities ## Angle Addition Identities $\sin A + \sin B = 2\sin \frac{1}{2}(A+B) \cos \frac{1}{2}(A-B)$ $\sin A - \sin B = 2\cos \frac{1}{2}(A+B) \sin \frac{1}{2}(A-B)$ # Derivations %%doing off memory but i don't like these :/%% # Example Questions # What's Next This isn't much of an education resource when it comes to the trigonometric identities themselves, but ideally this could serve as an alternative formula sheet to some other formula sheets out there. To actually dive into trigonometry proper, go take a look at[[The Unit Circle (Maths)| The Unit Circle]], a mastery of which is very, very important! To get back to the maths master page and browse other topics go here: [[Maths Contents Page]]