Re: trigonometric ratios
Do you know the identity:
\(\displaystyle tanx = \frac{sinx}{cosx}\) ?
If so, then what is sin45 and cos45 equal to?
If not, I'll prove it to you. Imagine a triangle \(\displaystyle \triangle ABC\) with sides a, b, c, \(\displaystyle \angle ACB\) is a right angle, and \(\displaystyle x = \angle ABC\)
Code:
A
*
**
* *
b * * c
* *
* *
* * * * * * B
C a
From that, we have by definition:
\(\displaystyle sinx = \frac{b}{c} \quad cosx = \frac{a}{c} \quad tanx = \frac{b}{a}\)
That means:
\(\displaystyle \frac{sinx}{cosx} = \frac{\:\frac{b}{c}\:}{\:\frac{a}{c}\:} = \frac{b}{c} \cdot \frac{c}{a} = \frac{bc}{ac} = \frac{b}{a} = tanx\)
\(\displaystyle \therefore tanx = \frac{sinx}{cosx}\)
