Graph Circles on a Graphing Calculator

Entering a circle into a graphing calculator can be accomplished by converting the circle to a polar equation and then entering it into the equation editor. Polar equations have an r variable, which is the radial coordinate and a dependent variable, and a θ, which is the angular coordinate and an independent variable. In standard form, a circle equation is written in the form (x - h)^2 + (y - k)^2 = r^2 where (h,k) is the center and r is the radius. An important circle is the unit circle which has the equation x^2 + y^2 = 1 and a radius of 1.

Instructions
1. Convert the expression to polar coordinates and simplify. To convert to polar coordinates, use the conversions x = r*cosθ and x = r*sinθ. For example, the unit circle would become (r*cosθ)^2 + (r*sinθ)^2 = 1. (r*cosθ)^2 + (r*sinθ)^2 is the same as r^2*cos^2(θ) + r^2*sin^2(θ). Pulling out the r^2 factor from both terms on the left-hand side of the equation gives r^2(cos^2(θ) + sin^2(θ)) = 1. By a Pythagorean identity in trigonometry, cos^2(θ) + sin^2(θ) = 1, so the equation becomes r^2 = 1.

2. Solve for the "r" variable. In the unit circle example, take the square root of both sides to get r = √(1).

3. Switch to polar mode on the calculator. On the TI-89, for example, you can do this by pressing the "Mode" button and then pressing arrow "->" key while on the "Graph" menu line. Press "3" to select "Polar." Press "Enter" to save the changes.

4. Enter the equation into the calculator's equation editor. For example, on a TI-89, press the green diamond button and then "F1." Type √(-x^2 + 1) after the "r1=."

5. View the graph. To do this on a TI-89, press the "Graph" button.

Write an Absolute Value on a Graphing Calculator

The absolute value of an integer is difference between the number and zero. For instance, both 8 and minus- 8 have absolute values of 8 because they are both eight spaces away from zero, albeit in opposite directions. In algebra, you may be required to solve equations with absolute values by graphing, or you might need to quickly calculate the absolute value of a numerical expression, such as -5(3)^31. When you are allowed to use a graphing calculator, it is important to understand how to write absolute value on it.

Instructions:

Finding the Absolute Value of a Number or Numerical Expression
1. Press the "ON" button in the lower left-hand corner of the calculator. Then, press the "MATH" button toward the upper left.

2. Use the right arrow to scroll sideways to the "NUM" selection. Then, either press "ENTER" in the lower right-hand corner of the keypad or the number 1 to select the absolute value function.

3. Type in the numerical expression. Then, insert a left-facing parenthesis, located in the middle of the keyboard, to close the absolute value. Hit "ENTER" to get the answer.
  
 Graphing an Absolute Value
1. Press the "ON" button in the lower left-hand corner of the calculator. Then, press the "Y=" in the upper left.

2. Select the "MATH" button and then scroll to the right using the directional arrow to select "NUM."

3. Press "ENTER" or 1. Type in the algebraic equation, such as X - 3. Use the variable button "X,T..." for any variables.

4. Close the equation with a left-facing parenthesis. Then, hit "GRAPH" in the upper right to display the graph of the equation.


Tips & Warnings
- Insert the absolute value before the number or expression that goes in it, not after.
- Type any coefficients or parts of the equation outside of the absolute value before you insert it. For instance, with 3abs(2X - 4), you type the 3, then perform the steps above.