• 021011 / Degree and Radian Measure 2 :) •

- This morning we discussed more about degrees, radians and formulas.  This is just a short summary of what we have so far in this unit.

「 * All in brackets are notes to be remembered. 」

We learned that:

• Two positive angles are supplementary if the sum of their measures is 180° or π.
• Two positive angles are complementary if the sum of their measures if 90° or π / 2.

Example: State the complement of 27° in both degree and radian measure.

「 * Complementary angles add up to 90°. 」 

Solution:

              90° - 27° = 63°

「 * Since 63° is in degrees, we need to convert it into a radian because we're looking for both degree and radian measure. 」

              63° • π / 180° 

              = 63π / 180 

              = 7π / 20

27° and 63° - or - 3π / 20 and  7π / 20 are complementary angles.

We also talked about different formulas such as:

• s = r • θ   
• r = s / θ  
• θ = s / r  
• Area of a Sector = θ • r² / 2

「 * Always remember that θ must be in radians to use any of these formulas. 」

Example: If the arc length is 81cm and the radius is 27cm, find the measure of the central angle to the nearest tenth of a degree.

 「 * Use diagrams or drawings to illustrate and understand the problem more. 」

「 * List all the given measures. 」

Given:

• s = 81cm
• r = 27cm
• θ = ?              

Solution:

           

              θ = s / r

              θ = 81cm / 27cm

              θ =  3 radians

 「 * Since our answer is in radians, we need to convert it into a degree. 」

              3 • 180° / π

              = 171.8873385°

              = 171.9°

The arc length is 3 radians - or - 171.9°.

「 * For more examples see notes and worksheets :) 」

- j a y m e e ♡