How do similar right triangles lead to the definitions of the trigonometric ratios?

Question

Cornelius Daniels

Mathematics

6 August, 04:42

How do similar right triangles lead to the definitions of the trigonometric ratios?

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Saige Mcdonald · Answer 1

The ratio of two sides of one right triangle is the same of the corresponding sides of any its similar triangles.

Call a, b, c the sides of a right triangle and A, B, C the sides of any of its similar triangles.

Then a/b = A/B, which means that this ratio is a constant.

The same for a/c = A/C, and b/c = B/C.

Even, the same is true for the inverses: b/a = B/A; c/b = C/B, and d/a = C/A.

Then, you can define a function for every one of these ratios. Those functions are the trigonometric functions.