Trigonometry

The unit circle

continues from lesson 1 — values defined earlier in the course stay live here

For angles beyond 90° the triangle picture breaks down, so trig moves to the unit circle: a circle of radius 1, where cos(φ) is the x-coordinate and sin(φ) the y-coordinate of a point at angle φ. One identity holds for EVERY angle — it is just Pythagoras in disguise:

\phi := 132 deg

= 132 deg any angle you like — even past 90°

✓ pass

\mathrm{abs}\left(\mathrm{sin}\left(\phi\right)^{2} + \mathrm{cos}\left(\phi\right)^{2} - 1\right) < 10^{-9}

sin² + cos² = 1, always

sqrt(1 - x^2)

upper half of the unit circle x² + y² = 1