One way of learning trigonometry is to define everything in terms of the unit circle, so it is helpful if we spend a few days on unit circle concepts before we introduce the trig functions.
The first thing we need to do is recall the equation of the circumference. The circumference of a circle is ____________ , so the circumference of the unit circle is ________.
The book defines radian measure, θ, formally for any circle as the ratio of the arc length, s to the radius, r, i.e.
1.) Fill in the missing piece of information for each of the following circular sections:
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On the unit circle an angle measured in radians would equal its ___________________ . We normally measure from the positive x-axis.
The following points on the unit circle will be used often in this class, since they make nice examples that can be worked out exactly. Fill in the labeled points and the points on the axis with their values in radians between 0 and 2π inclusive and then click here to check your answer.
Now since we measure counterclockwise from the positive x-axis to go in the positive direction, it only makes sense that we would measure clockwise from the positive x-axis to measure negative angles.
Find a.) -3π/4, b.) 17π/6, and c.) 7π on the unit circle. Answer
Recall that there are 360° in a one circle, so the conversion formula from radians to degress must be
When doing problems involving angular speed or circular linear speeds we can just treat them as conversion problems.
Example: Suppose a bicyclist's is riding at a rate of 15 miles per hour. The diameter of his tires are 27 inches.