- 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 ♡
No comments:
Post a Comment