Understanding the Pythagorean Theorem's Ratios

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The Pythagorean theorem, expressed as a² + b² = c², is foundational for understanding trigonometric ratios such as sine, cosine, and tangent. By assigning values to the sides of a right triangle—where 'a' is the opposite side, 'b' is the adjacent side, and 'c' is the hypotenuse—one can derive the trigonometric identities. Dividing the sides of the triangle by the hypotenuse leads to the definitions of sine (opposite/hypotenuse) and cosine (adjacent/hypotenuse), while tangent is defined as the ratio of sine to cosine. Resources like the Khan Academy can provide further clarification on these concepts. Understanding these relationships is crucial for mastering trigonometry.
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Homework Statement



How does the pythagorean therm. give us sin cos tan and their recipr.? I don't understand how a^2 + b^2 = c^2 give you those ratios?

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The pythagorean theorem will give you the pythagorean identities if you let a=opposite side b=adjacent side, c= hypotenuse. You can derive all the pythagorean identities by dividing by the different sides.

You may want to skim over this http://mathsfirst.massey.ac.nz/Trig/TrigRatio.htm or even better take a look at the khan academy library of videos on trig.
 
Thank you.
 

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