# 4: Trigonometric Identities and Equations

- Page ID
- 7117

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- 4.1: Trigonometric Identities
- An identity is an equation that is true for all allowable values of the variables involved. To prove that an equation is an identity, we need to apply known identities to show that one side of the equation can be transformed into the other. To prove that an equation is not an identity, we need to find one input at which the two sides of the equation have different values.

- 4.2: Trigonometric Equations
- A trigonometric equation is a conditional equation that involves trigonometric functions. If it is possible to write the equation in the form “some trigonometric function of x ” = a number.

- 4.5: Sum-Product Identities
- In general, trigonometric equations are very difficult to solve exactly. We have been using identities to solve trigonometric equations, but there are still many more for which we cannot find exact solutions.

*Thumbnail: Graphs of \(y=sin(2θ)\) and \(y=sin(θ)\).*