A graphical solution to an equation is a solution obtained by plotting the functions on both sides of the equation and finding the intersection points of the graphs.
Graphical solutions are approximations. They are notexactsolutions.
Solving Trigonometric Equations Graphically
Graphing Trigonometric Functions
To solve a trigonometric equation graphically, we need to plot the graphs of the functions on both sides of the equation.
1. Solve the equation $\tan(x) = 1$ for $0 \leq x < 2\pi$ graphically. 2. Find the solutions to $\sin(2x) = \cos(x)$ for $0 \leq x < 2\pi$ using a graphing calculator.
How does technology influence our understanding of mathematical solutions? Are graphical solutions as valid as algebraic ones?
Graphical solutions are approximations. Always verifythe accuracyof the solutionif exactvaluesare required.
1. How do graphical solutions compare to algebraic solutions in terms of accuracy and efficiency? 2. In what situations might a graphical solution be preferred over an algebraic one?
