Trigonometry Related Pages: 258-259 & 269-270 "Solving Trig and Inverse Trig Equations"
College Algebra and Trigonometry Related Pages: 595 & 603-604 "Solving Trig and Inverse Trig Equations"
Precalculus Related Pages: 511 & 519-520 "Solving Trig and Inverse Trig Equations"

Visually verify the algebraic solutions to trig and inverse trig equations by plotting the equation as a function. If you are solving 2 equations simultaniously then plot the equations as functions in the form y=f(x) and y=g(x). Plot your algebraic solution as a data point. If the solution is correct then the data point will appear at the intersection of y=f(x) with y=g(x).

If you are solving an equation equal to zero or another constant plot the equation as a function of the form y=f(x) and plot the data point (c, y) where c is the zero or constant and y is the solution to the equation. If the solution is correct then the data point will appear as a point on the function.

The main difference in the way the software works versus graphing by hand is the number of points plotted. Graphing by hand, you would probably plot 5 to 10 points and use our "math intuition" to connect the points appropriately. The computer plots many more points (depending on the x range, somewhere around 100) and connects the dots. This is how graphing calculators work, too.

This can lead to interesting behavior for certain functions. Polynomials like lines and parabolas will graph just as they should. Other functions, such as those for which x appears in a denominator, may have places on the graph where the computer has trouble plotting them correctly. This leads to the following moral: