Unit 3: Trigonometry (Math 20-1)
Angles & reference angles, CAST, special triangles & exact values, Sine and Cosine Laws, and the SSA ambiguous case.
Reference Angle
CAST
Special Triangles
Sine Law
Cosine Law
SSA Ambiguity
What You Should Be Able To Do
- Convert angles, find coterminal angles, determine the reference angle and quadrant (CAST).
- Use special triangles to find exact values of \(\sin,\cos,\tan\) for key angles.
- Apply the Sine Law and understand the SSA ambiguous case (0, 1, or 2 solutions).
- Apply the Cosine Law in SAS and SSS situations; solve entire triangles.
- Communicate results with appropriate rounding, units, and reasoning.
Progress autosaves to this device.
Video Library
Reference Angles & CAST
Reference angle, quadrant signs, coterminals.
youtube.com – “reference angle and CAST rule”Special Triangles & Exact Values
30-60-90 and 45-45-90 exact ratios.
youtube.com – “special triangles exact values 30 45 60”Sine Law & SSA Ambiguous Case
0, 1, or 2 triangles — when and why.
youtube.com – “sine law SSA ambiguous case”Cosine Law (SSS/SAS)
Find sides or angles when Sine Law won’t do.
youtube.com – “cosine law SSS SAS problems”Interactive Tools
Angle, Reference Angle & CAST
Special Triangles – Exact Values
| Ratio | Exact | Decimal |
|---|
Sine Law (AAS/ASA/SSA)
Use triangle \(ABC\) with sides \(a,b,c\) opposite \(\angle A,\angle B,\angle C\).
Cosine Law (SSS / SAS)
Enter any valid SSS or SAS set for triangle \(ABC\).
Unit 3 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: reference angle for \(-220^\circ\); exact \(\sin 30^\circ,\cos 45^\circ,\tan 60^\circ\); solve \(a=12, A=35^\circ, b=10\) (SSA); solve \(a=7,b=9,c=5\) (SSS).