Wednesday, October 4, 2017

trigonometry basics

Trigonometry ... is all abouttriangles.
Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more!

Right-Angled Triangle

The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner:
triangle showing Opposite, Adjacent and Hypotenuse
Another angle is often labeled θ, and the three sides are then called:
  • Adjacent: adjacent (next to) the angle θ
  • Opposite: opposite the angle θ
  • and the longest side is the Hypotenuse

Why?

Why is this triangle so important?
Imagine we can measure along and up but want to know the direct distance and angle:
triangle showing Opposite, Adjacent and Hypotenuse
Or we have a distance and angle and need to "plot the dot" along and up:
triangle showing Opposite, Adjacent and Hypotenuse
Questions like these are common in engineering, computer animation and more.
And trigonometry gives the answers!

Sine, Cosine and Tangent

The main functions in trigonometry are Sine, Cosine and Tangent
They are simply one side of a right-angled triangle divided by another.
For any angle "θ":
sin=opposite/hypotenuse cos=adjacent/hypotenuse tan=opposite/adjacent

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