Choose an exam and explore concepts through visual explanations, topic maps and revision checks. Open the full chapter notes whenever you need more detail.
THE VISUAL LEARNING STUDIO
See the idea. Understand the connection.
35 visual explanations across 29 chapters, with topic maps throughout the library.
The chapter index will grow as additional notes are prepared. Chapters shown here are a learning collection, not a claim that the entire exam syllabus is complete.
SEE IT. CONNECT IT. EXPLAIN IT.
Understand the chapter visually
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Study the expanded notes and the credited detailed textbook lessons. The current chapter index covers core topics; it is not a claim of exhaustive coverage of every examination syllabus. Check the official syllabus and primary references.
Trigonometry — lesson overview
Ratios and angles
For an acute angle in a right triangle, sine is opposite/hypotenuse, cosine adjacent/hypotenuse and tangent opposite/adjacent.
The unit-circle definition extends trigonometric functions beyond acute triangle angles and determines signs in different quadrants.
Degrees and radians are different angle units: π radians = 180°. Calculator mode must match the question.
Identities and domains
The identity sin²θ + cos²θ = 1 holds for real angles. Dividing by cos²θ gives 1 + tan²θ = sec²θ where cosθ is nonzero.
A derived identity retains the conditions of any division used. Tangent is undefined at angles where cosine is zero.
An identity is true for every value in its domain; an equation such as sinθ = 1/2 selects particular angles.
Worked reasoning
For an acute angle with sinθ=3/5, the adjacent side in a proportional right triangle is 4, giving cosθ=4/5 and tanθ=3/4.
The acute-angle condition selects the positive cosine; without quadrant information, sign choices need further consideration.
Periodic functions can have multiple solutions. State the interval or general solution rather than assuming every equation has one answer.
