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education/math/MATH1060 (trig)/Angles.md
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@ -19,13 +19,18 @@ A **supplementary** angle is formed when two positive angles add up to $180\degr
Angles greater than $90\degree$ have no complement and angles greater than $180\degree$ have no supplement. Angles greater than $90\degree$ have no complement and angles greater than $180\degree$ have no supplement.
# Right Angle Trigonometry # Right Angle Triangle Trigonometry
| SohCahToa | Inverse | | SohCahToa | Inverse |
| --------------------------------------------- | --------------------------------------------- | | --------------------------------------------- | --------------------------------------------- |
| $$ sin\theta = \frac{opposite}{hypotenuse} $$ | $$ csc\theta = \frac{hypotenuse}{opposite}$$ | | $$ sin\theta = \frac{opposite}{hypotenuse} $$ | $$ csc\theta = \frac{hypotenuse}{opposite}$$ |
| $$ cos\theta = \frac{adjacent}{hypotenuse} $$ | $$ sec\theta = \frac{hypotenuse}{adjacent} $$ | | $$ cos\theta = \frac{adjacent}{hypotenuse} $$ | $$ sec\theta = \frac{hypotenuse}{adjacent} $$ |
| $$ tan\theta = \frac{opposite}{adjacent} $$ | $$ cot\theta = \frac{adjacent}{opposite} $$ | | $$ tan\theta = \frac{opposite}{adjacent} $$ | $$ cot\theta = \frac{adjacent}{opposite} $$ |
| | | These rules apply regardless of the orientation of the triangle.
Cosecant, secant, and tangent are inverses of sine, cosine, and tangent respectively, and so they can be found by taking $\frac{1}{x}$, where $x$ is the function you'd like to find the inverse of.
# Definitions # Definitions
| Term | Description | | Term | Description |
@ -40,5 +45,6 @@ Angles greater than $90\degree$ have no complement and angles greater than $180\
| 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 is: <br><br>Complementary starts with C, and C stands for corner. $90\degree$ makes a corner. | | 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 $\pi$. 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. | | 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. |
| | | | Hypotenuse | The side opposite the right angle in a triangle. |
| | | | Opposite | |
| Adjacent | For a given angle $\theta$ in a right triangle, this side makes up the side of the intersection opposite the hypotenuse. |