Trigonometric Identities

 This problem set can be used immediately after the introduction of right triangle trigonometry. It only uses the Pythagorean identity, the definitions of secant, cosecant, and cotangent, and the fact that tanx=sinx/cosx. This problem set is not about proving identities but rather how to come up with them, using reference triangles. For example, writing cosx given tanx. It can be used after the introduction of right triangle trigonometry, and it is probably best before extending to the unit circle definition. These techniques come up again in trigonometry and also in calculus, when simplifying inverse expressions. Trigonometric identities that are consequences of the unit circle definitions. This problem set is sort of amending the basic identities, as they are modified by the introduction of the unit circle definition. For example, until now, when sinx was given to be 3/5, then we could compute that the cosine is then 4/5. In this handout, the answer to the same problem is 4/5 or -4/5. This can be introduced soon after the unit circle definition. This is a proof for the sum formulas for sine and cosine I found on Wikipedia. Assuming the sum formulas for sine and cosine, we derive all other compound angle formulas for sine, cosine, and tangent. Basic applications and a few identities are also included. Proving trigonometric identities that involve the compound angle formulas. There is no new material since trigonometric identities 3. This handout is just a response to my experience that students need more guidance or practice after the introduction of compound angle formulas.