Trigonometry recap

A right triangle and its relations are the basis of almost every physics problem: they are needed whenever we must resolve a vector quantity into its components.

Right triangle: hypotenuse $i$, adjacent side $a$ and opposite side $o$ with respect to angle $\alpha$.

In a right triangle with hypotenuse $i$, adjacent side $a$ and opposite side $o$ with respect to angle $\alpha$, the three fundamental relations hold:

$\cos\alpha = \frac{a}{i}, \qquad \sin\alpha = \frac{o}{i}, \qquad \tan\alpha = \frac{o}{a}$

Conversely, given a ratio between the sides, the angle can be found using the inverse functions:

$\alpha = \arctan\!\left(\frac{o}{a}\right) = \arcsin\!\left(\frac{o}{i}\right) = \arccos\!\left(\frac{a}{i}\right)$

These relations will be constantly needed to pass from the magnitude and direction of a vector to its Cartesian components, and vice versa.

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Topics: Vectors Skills: Use of trigonometry · Vector resolution

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