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education/math/MATH1060 (trig)/Angles.md
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@ -2,7 +2,17 @@ Angles consist of two rays with the same endpoint and are typically measured in
If an angle is measured counterclockwise, it's a *positive angle*, and if an angle is measured clockwise, it's a *negative angle*. If an angle is measured counterclockwise, it's a *positive angle*, and if an angle is measured clockwise, it's a *negative angle*.
## Complementary and Supplementary Angles
A **complimentary** angle is formed when two positive angles add up to $90\degree$ or $\frac{\pi}{2}$. One mnemonic device that you can use to remember this is:
> Complementary starts with C, and C stands for corner. $90\degree$ makes a corner.
A **supplementary** angle is formed when two positive angles add up to $180\degree$ or $\pi$. One mnemonic device that you can use to remember this is:
> Supplementary starts with S and S stands for straight. $180\degree$ makes a straight line.
Angles greater than $90\degree$ have no complement and angles greater than $180\degree$ have no supplement.
# Definitions # Definitions
| Term | Description | | Term | Description |
| -------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | | -------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
@ -14,5 +24,7 @@ If an angle is measured counterclockwise, it's a *positive angle*, and if an ang
| Terminal side | In standard position, the terminal side is the ray that's being measured relative to the initial side. | | Terminal side | In standard position, the terminal side is the ray that's being measured relative to the initial side. |
| $s$ | The length of a curve along the radius. | | $s$ | The length of a curve along the radius. |
| Radian | Denoted with $rad$, one radian is equal to the radius, but it's measured along the arc in a curve instead of from the center. | | Radian | Denoted with $rad$, one radian is equal to the radius, but it's measured along the arc in a curve instead of from the center. |
| Complementary Angles | Two positive angles that add up to $90\degree$ or $\frac{\pi}{2}$. One mnemonic device that you can use to remember this | | Complementary Angles | Two positive angles that add up to $90\degree$ or $\frac{\pi}{2}$. One mnemonic device that you can use to remember this is: <br><br>Complementary starts with C, and C stands for corner. $90\degree$ makes a corner. |
| Supplementary Angles | Two positive angles that add up to $180\degree$ or $\pi$. | | Supplementary Angles | Two positive angles that add up to $180\degree$ or $\pi$. One mnemonic device that you can use to remember this is:<br><br>Supplementary starts with S and S stands for straight. $180\degree$ makes a straight line. |
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