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### 8.10. Chapter 8 Summary and Highlights

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• This chapter includes a brief summary of important algebraic techniques that are applicable to solving equations and inequalities involving trigonometric and circular functions. Included are explanations of solving (1.) algebraic equations for an unknown variable, (2.) algebraic equations that contain fractions and combining fractions, (3.) algebraic equations that contain square roots, (4.) quadratic equations using the method of factoring, the quadratic formula, and the square-root method, (5.) algebraic inequalities, and (6.) algebraic equations and inequalities using graphing.

• Equations and inequalities containing trigonometric or circular functions can be solved using a number of techniques. There is often more than one method that can be used to solve a given trigonometric equation, and in addition, combining several techniques may be necessary for solving more complex equations and inequalities. Trigonometric equations and inequalities can be solved using techniques such as: factoring, substituting into the quadratic formula, substituting identities, standard position angles and reference triangles, the location of a point on a unit circle, and using graphical techniques such as the x-intercept and intersection-of-graphs methods. When an equation or inequality cannot be solved analytically using algebra, it may be solved (or the solutions estimated) graphically.