This part of the unit is really about equivalence:

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Presentation transcript:

This part of the unit is really about equivalence: ?

Remember: And because we are dealing with the unit circle here, we can say that for this special case,

Remember: Recall the formula for arc length Since 30° is of the way around, then the length of this arc is arc length arc length = arc length So for any radius r when the central angle is 30° the length of the arc is…

Remember: Since 45 is arc length of the way around, then the length of this arc is arc length = arc length So for any radius r when the central angle is 45

Remember: Since 60 is arc length of the way around, then the length of this arc is arc length = arc length So for any radius r when the central angle is 60

We now can measure angles with a new unit of measurement: Radians Recall how to cancel units from science classes?

We now have this ratio: Converting degrees to radians Converting radians to degrees Multiply by Multiply by To sum this up, in PreCalc and beyond you’ll see how important radian measurements are in math. The first direct application we’re seeing here is how they are the direct way to translate angle measurements into arc lengths.

Convert to radians Convert to degrees Notice that the radian problems on the right don’t have units. For reasons we won’t discuss here, angle measurements without units are assumed to be radians.