The formula for the distance between two points in the xy-plane is based on the Pythagorean theorem. (You also need to know how to compute the distance between points on the same horizontal or vertical line.)
        
 

It's easy enough to compute distances between points each time you need one just by typing the appropriate expression into the calculator. Here's a way to do it once and have it available whenever you need it. We'll define our own function and call it dist. We want dist(x₁, y₁, x₂, y₂) to give the distance between the point (x₁, y₁) and the point (x₂, y₂).

Once you've defined the funciton, if you want to know the distance between (1,2) and (3,-4), just go to the command line and type dist(1,2,3,-4) and ENTER. 

1. Find the distance between the points (2.714, -3.518) and (0.488, 1.631).

2. Define and store a function that computes the slope of the line through two given points. Try it with some points and compare with hand calculations to make sure it's working correctly.

3. Find an equation for the line through the points (2.714, -3.518) and (0.488, 1.631).

4. You could automate the whole process for exercise 3: your function should take 4 coordinates as inputs and produce an equation as output.

5. TI calculators come equipped with sine, cosine, and tangent functions, but not with secant, cosecant, or cotangent functions. Define them and store them in your calculator.

6. Graph your "new" trigonometric functions. (Use ZoomTrig.)

Remember that you ALWAYS want to use radians for trig functions in calculus.
 
 

It is possible to find distances between points in the GRAPH screen. They need to be points on the graph of some function(s) you've drawn, so that the cursor can find them. The command is on the Math menu (F5).

You can also use the Data/Matrix editor to find equations for lines. Put the x-coordinates in c1, y in c2, and use LinReg in the Calc menu (F5).

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