George W. Ferris' Day Off and Sine Language

Learning Focus

  • Applying right triangle trigonometry in circular contexts.
  • Using trigonometry to find distances.

Lesson 1 Takeaways

  • Right triangles in circles: Vertical distance from center.
  • Ferris wheel height: Height=30±25sin⁡(θ)Height = 30 \pm 25 \sin(\theta)
  • Finding y: y=r⋅sin⁡(θ)y = r \cdot \sin(\theta)

IM3 Unit 6 Angle Vocab

  • Initial Side: Angle's starting position.
  • Terminal Side: Angle's ending position.
  • Standard Position: Vertex at origin, initial side on +x-axis.
  • Coterminal Angles: Share terminal side (±360∘\pm 360^\circ).
  • Positive/Negative Angles: Counterclockwise/clockwise rotation.
  • Reference Angles: Acute angle between terminal side and x-axis.

Right Triangle Trig

  • Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2
  • Trig Ratios: SOH CAH TOA
    • $$\\sin(\theta)