This Crash Course video is a review of trigonometry, so you'll need to be familiar with a few concepts before you start watching. You should know how to differentiate between different types of triangles in order to correctly apply the various concepts related to trigonometry. You should also know how to calculate the area of a triangle and how to apply the Pythagorean Theorem. Lastly, it's important to ensure your calculator is in degree mode when working with trigonometric ratios.
Here are some rules and tips to remember:
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To use the trigonometric ratios (sine, cosine and tangent), it's important that the triangle is a right triangle and that the sides are clearly identified: opposite or adjacent to the angle in question and the hypotenuse.
Be careful! The adjacent and opposite sides depend on the angle that you're working with. -
Here are the trigonometric ratios:||\begin{align}\sin\theta&=\dfrac{\text{Measure of the leg opposite angle }\theta}{\text{Measure of the hypotenuse}}\\\\\cos\theta&=\dfrac{\text{Measure of the leg adjacent to angle }\theta}{\text{Measure of the hypotenuse}}\\\\\tan\theta&=\dfrac{\text{Measure of the leg opposite angle }\theta}{\text{Measure of the leg adjacent to angle}}\end{align}||
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SOH-CAH-TOA is a mnemonic device to help you remember these ratios.
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Sometimes it's faster and easier to use the Pythagorean Theorem to solve a right triangle.
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When using the Law of Sines, be sure to match each angle with its opposite side:||\begin{gather}\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\\\\text{OR}\\\\\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\end{gather}||Be careful! Don't forget that if you're looking for an obtuse angle, you must subtract the acute angle from 180°.
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When using the Law of Cosines, it's important to ensure the angle lies between two sides whose measurements are known. In addition, it's possible to use the Law of Cosines when you know the measurements of all 3 sides of the triangle.||a^2=b^2+c^2-2bc\cos A||
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There is more than one way to calculate the area of a triangle.
Given information
Formula to use
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A base |(b)|
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The height relative to this base |(h)|
Traditional formula||A=\dfrac{b\times h}{2}||
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2 sides |(a| and |b)|
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The angle |(C)| that lies between these sides.
Trigonometric formula||A=\dfrac{a\times b\times\sin C}{2}||
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All 3 side measurements of a triangle |(a, b| and |c)|
Heron’s formula||\begin{gather}A=\sqrt{p(p-a)(p-b)(p-c)}\\\\\text{where}\\\\p=\dfrac{a+b+c}{2}\end{gather}||
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