From 7ce0a42856f300c9569d1701499acfbf6de8e275 Mon Sep 17 00:00:00 2001 From: zleyyij <75810274+zleyyij@users.noreply.github.com> Date: Wed, 4 Sep 2024 10:28:39 -0600 Subject: [PATCH] vault backup: 2024-09-04 10:28:39 --- education/math/MATH1060 (trig)/Angles.md | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/education/math/MATH1060 (trig)/Angles.md b/education/math/MATH1060 (trig)/Angles.md index af19aa0..855c867 100644 --- a/education/math/MATH1060 (trig)/Angles.md +++ b/education/math/MATH1060 (trig)/Angles.md @@ -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. -# Right Angle Trigonometry +# Right Angle Triangle Trigonometry + | SohCahToa | Inverse | | --------------------------------------------- | --------------------------------------------- | | $$ sin\theta = \frac{opposite}{hypotenuse} $$ | $$ csc\theta = \frac{hypotenuse}{opposite}$$ | | $$ cos\theta = \frac{adjacent}{hypotenuse} $$ | $$ sec\theta = \frac{hypotenuse}{adjacent} $$ | | $$ tan\theta = \frac{opposite}{adjacent} $$ | $$ cot\theta = \frac{adjacent}{opposite} $$ | -| | | +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 | 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. | | 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:

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:

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. |