DWG NO. 06 — Unit 6 of 10
6 online lessons · 1 in-person Review & Practice Day
Units 4 and 5 built trigonometry on the unit circle and on right triangles, but most triangles you'll meet — in surveying, navigation, engineering — aren't right triangles at all. This unit opens with two tools for solving any triangle from partial information: the Law of Sines and the Law of Cosines, plus a way to find a triangle's area without ever finding its height.
The back half turns to two ideas that reuse the same trigonometric machinery in a new setting. Vectors use magnitude and direction — not just x and y — to describe quantities like force and velocity, and polar coordinates locate a point by a distance and an angle instead of two perpendicular distances. Both lean directly on the sine and cosine relationships from Unit 4.
Law of Sines
Solving oblique triangles (AAS, ASA, SSA) and recognizing the ambiguous SSA case.
→Law of Cosines
Solving oblique triangles (SAS, SSS) where the Law of Sines doesn't apply directly.
→Area of a Triangle
The trig area formula ½ab sinC and Heron's Formula for area from three sides alone.
→Introduction to Vectors
Representing vectors in component form and finding magnitude and direction angle.
→Vector Operations and Applications
Adding, subtracting, and scaling vectors, and using them to model forces and velocities.
→Polar Coordinates and Polar Graphs
Converting between polar and rectangular coordinates and graphing basic polar curves.
→Review & Practice Day 6 — bring your questions from lessons 6.1–6.6. You'll work practice problems, get feedback, and take the Unit 6 test.