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Right Triangles - Sine and Cosine

939 views · Published 7 November 2012 · 3:09 · Indexed 10 November 2026

Channel: MooMooMath and Science · 2012 · Education

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Learn how to set up sine and cosine in trigonometry. 

Transcript
Setting Up Sin/Cosine
 Today we are going to set up and find sin and cosine. Let's review, the Sin of an acute angle equals opposite over hypotenuse. The cosine of an acute angle equals adjacent over hypotenuse. How do we decide which side is which? First let's look at angle A from angle a we have to look at our reference sides. If we go to our opposite side that will be our opposite side and I will label this o for opposite. The hypotenuse (labeled h) is always across from the fight angle so the adjacent or next to angle A. (labeled a) Now let's add some measurements. Let's say the opposite side is 6 and the hypotenuse is 10 in order to find my sin it will be the opposite over hypotenuse so the Sin of angle A will equal 6/10 which is my opposite over hypotenuse. The cosine is the adjacent over the hypotenuse I don't know the length of a so I can use the Pythagorean Theorem to find this side. So I will take a squared plus b squared which is 6 plus c which is 10 squared so to write this out I get a^2+6^2=〖10〗^(2 ) which becomes a^2+36=100 so a^2 equals 64 so a must be the length of 8 (take the square root of 64) I can now solve for A The Cos of A will be 8 over 10 because it is adjacent over hypotenuse and that is how I would solve. You can also look from angle B the opposite side would be the lower angle here, the adjacent is here and the hypotenuse is always opposite the right angle. So the opposite and adjacent will flip according to which angle. Hope this was helpful. 

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