Trigonometry

Comprehensive trigonometry course covering function graphs, transformations, and identities. Master sine, cosine, and tangent functions, learn graph transformations from basic forms to complex equations, understand asymptotes and periodicity, and explore reduction formulas and trigonometric identities.

1. Sine Function Graphs

Master sine function graphs from y = sin x to y = A sin(ωx + φ) + b. Learn domain, range, periodicity, symmetry, monotonicity, and graph transformations.

2. Cosine Function Graphs

Master cosine function graphs from y = cos x to y = A cos(ωx + φ) + b. Understand even function properties, symmetry, transformations, and relationship to sine.

3. Tangent Function Graphs

Master tangent function graphs from y = tan x to y = A tan(ωx + φ) + b. Understand vertical asymptotes, period π, domain restrictions, and unique properties.

4. Induction (Reduction) Formulas

Transform any angle of the form ±α + k·π/2 into a function of an acute angle α. Learn the name-change rule and how to determine signs by quadrant.

5. Sum and Difference Identities

Master the addition and subtraction formulas for sine, cosine, and tangent. Learn auxiliary angle formulas and their applications.

6. Identity Transformations

Master double angle, half angle, sum-to-product, product-to-sum, and triple angle formulas. Essential identities for solving complex trigonometric problems.

📊Practice: Function Graphs

15 comprehensive questions on sine, cosine, and tangent function properties

Test your knowledge of domain, range, periodicity, symmetry, and monotonicity for trigonometric functions.

🎯Practice: Induction (Reduction)

10 single-choice questions on odd/even name rule and quadrant signs

Practice reductions for sin, cos, and tan in both radians and degrees with instant feedback and explanations.

➕Practice: Sum & Difference

8 focused questions on addition and subtraction formulas

Master sine, cosine, and tangent sum and difference identities with practical applications.

📐Practice: Identity Transformations

12 comprehensive questions on double angle, half angle, and more

Test your mastery of trigonometric identity transformations including sum-to-product and triple angle formulas.

📈Function Calculator

Calculate properties of y = A sin(ωx + φ) and y = A cos(ωx + φ)

Interactive calculator for period, range, extrema, symmetry axes, centers, and monotonic intervals.

🧮Induction (Reduction) Calculator

Build ±α + k·π/2 and reduce trig functions step-by-step

Use the interactive calculator to apply the odd/even rule and quadrant signs to any expression.

🔢Sum & Difference Calculator

Calculate sin(α ± β), cos(α ± β), and tan(α ± β) formulas

Apply sum and difference formulas with step-by-step calculations and numerical results.

⚡Identity Transformation Calculator

Calculate double angle, half angle, and sum-to-product formulas

Interactive calculator for all trigonometric identity transformations with step-by-step solutions.