DWG NO. 04 — Unit 4 of 10
6 online lessons · 1 in-person Review & Practice Day
Every function in Units 1–3 was built from algebra: powers, products, and inverses of x. Trigonometry starts somewhere completely different — a point moving around a circle. As that point sweeps around, its coordinates rise and fall in a smooth, repeating rhythm, and that rhythm is exactly what sine and cosine measure. This unit builds the unit circle from the ground up, connects it back to the right-triangle ratios from geometry, and then turns the circle into six new functions with their own distinctive graphs.
Everything here is periodic — it repeats — which is a genuinely new kind of behavior compared to the polynomials and exponentials already covered. By the end of the unit you'll be able to read an angle in either degrees or radians, evaluate any trig function at any special angle without a calculator, and graph a transformed sine or cosine wave just as fluently as you graphed a shifted parabola back in 1.4.
Angles, Degree and Radian Measure
Angles in standard position, coterminal angles, and converting between degrees and radians.
→The Unit Circle and Special Angles
Defining sine and cosine as coordinates on the unit circle, and evaluating them at special angles.
→Right-Triangle Trigonometry Revisited
SOH-CAH-TOA, the six trig ratios, and how they connect to the unit-circle definitions.
→Graphing Sine and Cosine Functions
The wave shape of y = sin x and y = cos x, key points, domain, range, and period.
→Graphing Other Trig Functions
Tangent, cotangent, secant, and cosecant — their asymptotes, periods, and shapes.
→Amplitude, Period, Phase Shift, and Vertical Shift
Reading and graphing y = a sin(b(x − h)) + k as a transformation of the parent wave.
→Review & Practice Day 4 — bring your questions from lessons 4.1–4.6. You'll work practice problems, get feedback, and take the Unit 4 test.