Trigonometry and Measure of Angles
Radians, exact trigonometric values, the unit circle, trigonometric graphs, and angle-measure practice.
Active lessons
15
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
15 of 15 active
Lesson 1
Degrees and Radians
Understand what a radian is, learn the benchmark radian-degree equivalences, and identify quadrants using radian boundaries.
Lesson 2
Converting Degrees to Radians
Multiply by π/180 to convert any degree measure to an exact radian fraction and simplify.
Lesson 3
Converting Radians to Degrees
Multiply by 180/π to convert any radian measure to degrees, cancelling π to get a pure number.
Lesson 4
Arc Length
Apply s = rθ to find arc lengths, radii, and angles — converting degree angles to radians first when needed.
Lesson 5
Sector Area
Apply A = ½r²θ to find sector areas, radii, and angles, and calculate the perimeter of a sector.
Lesson 6
Exact Trigonometric Values
Derive and recall exact sin, cos, and tan values for π/6, π/4, and π/3 using the 30-60-90 and 45-45-90 special triangles.
Lesson 7
The Unit Circle and Exact Values
Use the unit-circle rule (cos θ, sin θ) to read exact trigonometric values at common Q1 and axis angles.
Lesson 8
Exact Values in All Quadrants
Use reference angles and ASTC to evaluate exact sin, cos, and tan values for angles in Q2, Q3, and Q4.
Lesson 9
Graphs of Sine, Cosine and Tangent
State and apply the period, range, starting value, zeros, maxima, minima, and asymptotes of y = sin x, y = cos x, and y = tan x.
Lesson 10
Amplitude and Period of Trigonometric Graphs
Identify and calculate the amplitude |a| and period 2π/b of y = a sin(bx) and y = a cos(bx).
Lesson 11
Transformations of Trigonometric Graphs
Identify amplitude, period, phase shift (−c/b), and vertical shift (d) of y = a sin(bx + c) + d, and state the new range.
Lesson 12
Right-Angle Trigonometry — Applications
Apply SOH CAH TOA to multi-step 2D problems; interpret and calculate angles of elevation and depression; read and write true bearings and compass bearings.
Lesson 13
Sine Rule, Cosine Rule and Area Formula
Apply the sine rule a/sinA = b/sinB and cosine rule a² = b² + c² − 2bc cosA to non-right-angled triangles; use Area = ½ab sinC; choose the correct rule for a given triangle.
Lesson 14
The Ambiguous Case of the Sine Rule
Determine how many triangles exist given SSA information; identify the ambiguous case condition bsinA < a < b; find both possible triangles when the ambiguous case applies.
Lesson 15
Trigonometry and Measure of Angles Exam Practice
Practise trigonometry and measure of angles exam practice with concise examples and mastery checks.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.