Suffolk Fall 08 Math 165 Lecture 3: Putting Descartes Before the Horse

Today, we finished going over analytic geometry, covered some basic trigonometry and gave the definition and properties of exponential and logarithmic functions. In the first third, we saw how to find the midpoint of a line segment given the coordinates of the endpoints, we talked about the different forms for the equation of a line (point-slope, slope-intercept) and we defined the slope. We also gave the equation a circle using the center and radius to completely determine the circle. In the second third, we defined trigonometric functions in two different ways; the first way used a right triangle, the second used the unit circle. We also used the equation of a circle to prove the useful trig identity
sin^2 x + cos^2 x = 1. Finally, in the last third we talked about exponential functions and noted that if we restrict the range to the set of positive real numbers, then they are bijections and hence have an inverse function. This inverse function is the logarithm. We talked about how properties of exponential and logarithmic functions translate across said bijection.

Category:

Education

Tags:

• precalculus
• analytic geometry
• trigonometric functions
• exponential functions
• logarithmic functions
• circles
• inverse functions math