So, then you can also say that these trig functions are the reciprocal of the basic trigonometric functions. The same thing applies to secant and cotangent: they are the reciprocal ratio of the sides that define the basic trig identity. (Remember SOHCAHTOA!) If you invert this ratio to be hypotenuse over opposite, this is the definition of cosecant. a2 b2 +c2 2 b c cos b2 a2 +c2 2 a c cos c2 a2. If you look at the definition of sine, you see that it is the ratio of opposite over hypotenuse. tan 2 r 1+cos 1 cos Other Useful Trig Formulas Law of sines 33. I'll refer you to my post on sine, cosine, and tangent for their basic definitions, as I will build upon those. This cheat sheet mainly focuses on trigonometric identities and inequalities involving. It covers a special case of trigonometric identities, in which a particular relation between the angles involved is known. These may be familiar to you already, especially if you have been introduced to the trig functions secant, cosecant, and cotangent. This cheat sheet covers the high school math concept Conditional Trigonometric Identities. If you know them and can recognize them automatically, your math homework and trigonometry questions will become a lot easier.įor the first set of trig identities, I will list the Reciprocal Identities. Trig identities are extraordinarily important in helping you solve your mathematics questions, and so the identities that I list and explain on this trig identities cheat sheet should really be committed to memory. Trigonometry Trig Cheat Sheet Definition of the Trig Functions Right. Think of them as a type of "constant" that can be swapped into expressions (that use sine, cosine, tangent, or any of the related trig functions secant, cosecant, or cotangent) to change their appearance without changing the math surrounding the expression. Trigonometry Essentials Practice Workbook with Answers: Master Basic Trig. They are incredibly valuable to understand and to memorize, and their usefulness becomes apparent when you are faced with a complicated trigonometric expression that needs to be simplified.Īll you need to do is rearrange the complicated trig expression such that you can express it in terms of the trigonometric identities, substitute in the identity to simplify, and carry on with solving the math problem. The trig identities are true for all values of the variable. This is your trig identities cheat sheet! Trig identities are defined as mathematical expressions that relate various trigonometric functions to others, regardless of what the variables are. Prove the following trig identities using only cos2(x) + sin2(x) 1 and sine and.