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Handout Wednesday 9/24
Let’s pick up where we left off with our review of basic trigonometry.
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First we want to switch to using radians. What do those means? 1 radian is the angle that gives you an arc of the circle of length equal to the radius of the circle.
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The key thing though is that the circumference of a circle is \(\2\pi r\text{,}\) so the full angle of a circle gives an arc length of \(2\pi\) times the radius. Thus a full circle (\(360^\circ\)) is \(2\pi\) radians.
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From this, we can divide a circle into smaller chunks. Half a circle is \(\pi\) radians, etc.
Now we can think of both \(\sin(x)\) and \(\cos(x)\) as being functions of \(x\text{.}\) But here \(x\) is the angle and \(y = f(x)\) is the value of the function (which is an \(x\) or \(y\) value on the unit circle). Let’s graph those functions.
Now what about the rate of change of those functions? Think about what increasing from 0 to 1 radian does to the \(x\) and \(y\) values on the unit circle!
We can also look at this graphically, by considering slopes of the sine and cosine functions.
Now let’s see how to combine all the rules we have so far. Work through the activity.
