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Trigonometric values, graphs, identities and equations topic check

Practise trigonometric values, graphs, identities and equations in G3 Additional Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals

Produce all six exact signed trigonometric values
Produce exact principal inverse trigonometric values
Produce complete exact trigonometric solution sets on stated intervals
Express a cos x + b sin x in R form and find its greatest and least values
Express a cos x + b sin x in R form and solve an equation in an interval
Give the amplitude, period and range of a trigonometric graph from its equation
Simplify a trigonometric expression using the standard identities
Interpret and graph trigonometric functions
Transform and justify trigonometric identities
Formulate, use and interpret a mathematical model

G3 Additional Mathematics 2027

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Choose a practice setProduce all six exact signed trigonometric values · 3 questionsProduce exact principal inverse trigonometric values · 3 questionsProduce complete exact trigonometric solution sets on stated intervals · 5 questionsExpress a cos x + b sin x in R form and find its greatest and least values · 2 questionsExpress a cos x + b sin x in R form and solve an equation in an interval · 2 questionsGive the amplitude, period and range of a trigonometric graph from its equation · 3 questionsSimplify a trigonometric expression using the standard identities · 2 questionsAll skills in this check

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Produce all six exact signed trigonometric values · Check your progress

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Produce exact principal inverse trigonometric values · Check your progress

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Produce complete exact trigonometric solution sets on stated intervals · Check your progress

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Express a cos x + b sin x in R form and find its greatest and least values · Check your progress

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Express a cos x + b sin x in R form and solve an equation in an interval · Check your progress

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Give the amplitude, period and range of a trigonometric graph from its equation · Check your progress

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Simplify a trigonometric expression using the standard identities · Check your progress

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Check again

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Produce all six exact signed trigonometric values · Check again

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Produce exact principal inverse trigonometric values · Check again

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Produce complete exact trigonometric solution sets on stated intervals · Check again

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Express a cos x + b sin x in R form and find its greatest and least values · Check again

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Express a cos x + b sin x in R form and solve an equation in an interval · Check again

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Give the amplitude, period and range of a trigonometric graph from its equation · Check again

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Simplify a trigonometric expression using the standard identities · Check again

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Retention check

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Produce all six exact signed trigonometric values · Retention check

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Produce exact principal inverse trigonometric values · Retention check

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Produce complete exact trigonometric solution sets on stated intervals · Retention check

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Express a cos x + b sin x in R form and find its greatest and least values · Retention check

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Express a cos x + b sin x in R form and solve an equation in an interval · Retention check

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Give the amplitude, period and range of a trigonometric graph from its equation · Retention check

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Simplify a trigonometric expression using the standard identities · Retention check

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Practise: Produce all six exact signed trigonometric values

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Practise: Produce exact principal inverse trigonometric values

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Practise: Produce complete exact trigonometric solution sets on stated intervals

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Practise: Express a cos x + b sin x in R form and find its greatest and least values

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Practise: Express a cos x + b sin x in R form and solve an equation in an interval

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Practise: Give the amplitude, period and range of a trigonometric graph from its equation

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Practise: Simplify a trigonometric expression using the standard identities

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Revision notes

Revise trigonometry

Explain signed trigonometric values and identities, interpret periodic models and solve equations on stated intervals in G3 Additional Mathematics.

Key ideas

Unit circle and inverse values
Use signed unit-circle coordinates and exact ratios, then select principal inverse values without losing the original angle context.
Trigonometric graphs and models
Read input/output scaling, preserve tangent discontinuities and infer a bounded periodic model with correct phase units.
Trigonometric identities and proof
Derive exact values and identities, justify cancellations on the original domain and distinguish a proof from isolated checks.
Interval equations and R form
Track transformed intervals, preserve zero factors and use signed R forms to solve equations and justify restricted ranges.

What the syllabus asks

From the G3 Additional Mathematics 2027 syllabus

Six trigonometric functions for angles of any magnitude (in degrees or radians)
Principal values of sin⁻¹x, cos⁻¹x, tan⁻¹x
Exact values of the trigonometric functions for special angles (30°, 45°, 60°) or (π/6, π/4, π/3)
Amplitude, periodicity and symmetries related to sine and cosine functions
Graphs of y = a sin(bx) + c, y = a sin(x/b) + c, y = a cos(bx) + c, y = a cos(x/b) + c and y = a tan(bx), where a is real, b is a positive integer and c is an integer
Use of: sin A/cos A = tan A; cos A/sin A = cot A; sin² A + cos² A = 1; sec² A = 1 + tan² A; cosec² A = 1 + cot² A; expansions of sin(A ± B), cos(A ± B), tan(A ± B); formulae for sin 2A, cos 2A, tan 2A; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α)
Simplification of trigonometric expressions
Solution of simple trigonometric equations in a given interval (excluding general solution)
Proofs of simple trigonometric identities
Use of trigonometric functions as models