a is the opposite side(adsbygoogle = window.adsbygoogle || []).push({});

b is the adjacent side

c is the hypotenuse.

x is the angle

Problem: expression for sin x as a function of a and c.

Solution:

Identities taken from textbooks:

sin x = a/b (1)

tan x = a/c (2)

sin x = sqrt(tan^2 x / (1 + tan^2 x)) (3)

substituting (2) in (3), we have

sin x = a / sqrt(a^2 + c^2) (4)

On the other hand,

a^2 + b^2 = c^2 => b=sqrt(c^2 - a^2)

substituting this in (1), we have

sin x = a / sqrt(-a^2 + c^2) (5)

(4) != (5) ????? how come?

What's wrong here, please?

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# Apparent trigonometric inconsistencies

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