Trigonometric functions

标签（空格分隔）： 三角函数

Unit right-angle triangle{#1}

\(\sin\theta=\frac{opposite \quad side}{hypotenuse}\)

\(\cos\theta=\frac{adjacent \quad side}{hypotenuse}\)

\(\tan\theta=\frac{opposite}{adjacent}\)

We can only define how many each trigonometric functions are with \(0\leq\theta\leq180^{\cdot}\).

unit circleUnit right-angle triangle^[1]

convert degree to radian

Instead, it measures the length of the arc corresponding to the \(\theta\), and the radian \(\theta\) can work!
$180^{\circ}=2\pi $

1 radian = \(\frac{180^{\circ}}{2\pi}\)

we can analogize triangle to circle where \(\theta\) can up to \(360^{\circ}\) or even \(n\times 360^{\circ}\).

\(\sin\theta=\frac{opposite \quad side}{hypotenuse}=y\)

\(\cos\theta=\frac{adjacent \quad side}{hypotenuse}=x\)

\(\tan\theta=\frac{opposite}{adjacent}=\frac{y}{x}\)

signs of trigonometric functions