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.
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