Today's soundtrack is Christafari: Valley of Decision, a reggae album that I've loved since I first got the album from a high school friend.
Today, I'm learning how to use technology to solve trigonometric equations. I started the lesson by watching this video, which covered the two basic ways of solving trig equations that equal each other (graphing them as two separate functions, or moving everything onto one side so that y = 0 and finding the zeros).
But let's back up a bit. Solutions are intersects: places where graphs meet. We can sketch any function, set up a straight line of y=value, and whenever the first function crosses that value, the x-value is a solution.
Let's say we want to solve an equation. We can plug both sides of it into the y= graphing section, find the intercepts, and call it a day. But what if we want to find all possible solutions? To do that, we need the general solution: an equation that we can plug any number into and still get a true solution. We can determine the general solution for an equation by adding the solution's value to n[period].
That's it for today! Next time, we'll work on solving trig equations for exact values without using a calculator.