How did the Ancient Greeks map the stars and constellations in respect to earth without modern technology? How can architects build buildings with intricate designs while remaining structurally sound? They used the mathematical ideas of trigonometry and the trigonometric identities to explore and manipulate the world around them. This website includes information on the history of trigonometric identities and the proofs of the most common trigonometric identities and how they interact with each other. It will also include an exploration of the relationship between the unit circle and the identities. Lastly it will include real-world applications of trigonometric identities to gain an appreciation of trigonometry. The application page will include a variety of applications that are found in stem fields as well as the creative arts fields. The image below is a general list of the commonly used trigonometric identities. The proofs page will highlight the pythagorean identities, sum and difference of cosine and sine, the double angle identities, and sum to product identities.