Trigonometric and Polar Functions

Fifteen topics on periodic change. The unit circle as the engine behind sine, cosine, and tangent, sinusoidal functions with amplitude, midline, period, and phase, transformations and context modeling, the tangent and reciprocal functions, inverse trig with its restricted ranges, equation solving that keeps every solution, and polar coordinates with the curves they draw.

Topics

3.1

Periodic Phenomena

Sine, Cosine, and Tangent

Sine and Cosine Function Values

Sine and Cosine Function Graphs

Sinusoidal Functions

Sinusoidal Function Transformations

Sinusoidal Function Context and Data Modeling

The Tangent Function

Inverse Trigonometric Functions

Trigonometric Equations and Inequalities

The Secant, Cosecant, and Cotangent Functions

Equivalent Representations of Trigonometric Functions

Trigonometry and Polar Coordinates

Polar Function Graphs

Rates of Change in Polar Functions

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

General sinusoid

f(x) = a·sin(b(x − h)) + k

Amplitude

|a| (distance midline to peak, never negative)

Period

2π/|b| for sin and cos; π/|b| for tan

Midline

y = k

Phase shift

h, read only AFTER factoring b out of the argument

Pythagorean identity

sin²θ + cos²θ = 1

Tangent

tan θ = sin θ / cos θ (undefined where cos θ = 0)

Polar to rectangular

x = r·cos θ, y = r·sin θ

Rectangular to polar

r² = x² + y², tan θ = y/x (quadrant-checked)

Inverse trig ranges

arcsin: [−π/2, π/2] · arccos: [0, π] · arctan: (−π/2, π/2)

Unit 3 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 15 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

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Check what stuck.

Units 1 through 3, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 40-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 40questions

44topics

43codes covered

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