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Mathematics · Year 10 · Path · MA5-TRG-P-02

Trigonometry D

Eight lessons that move trigonometry off the right triangle and onto the circle. Once an angle can be any size, the ratios become functions with graphs, a single ratio stops naming a single angle, and questions gain a second answer you have to go looking for.

8lessons
12syllabus points
6hstudy
Start Lesson 1 →
1
The Unit Circle
Sine and cosine redefined as the coordinates of a point, so any angle qualifies
2
Tangent and the Exact Ratios
Tangent as sine over cosine, and the two triangles worth memorising
3
Angles of Any Magnitude
Quadrant signs, related angles, and what happens past one full turn
4
Graphs of the Trigonometric Functions
Two waves and a broken curve, each read straight off the circle
5
Supplementary and Complementary Angles
Reflect the circle point across an axis and read what survives the move
6
Solving Trigonometric Equations
Size gives the related angle, sign gives the quadrants, the interval decides
7
The Ambiguous Case
Two triangles, one set of measurements, and the one line of arithmetic that separates them
8
Gradient and the Angle of Inclination
Rise over run is opposite over adjacent, so gradient is a tangent

Focus Area Snapshot

8lessons
12syllabus points
24worked examples
64questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Advanced in Year 11. The unit circle is the definition of sine and cosine used for the rest of senior mathematics, and the habit built here, of asking whether a ratio names more than one angle, is what keeps later solutions complete.

Start Lesson 1 →