Alphabeta MathFundamental Trigonometric Identities: Examples and Counterexamples
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✓ 6 results · all verified · 0 also independently AI-judged
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1 · Prerequisites
Abstract Algebra
Linear Algebra
Real Analysis
- Absolute and Conditional Convergence; Rearrangement; Products
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Continuity, IVT, EVT, and Uniform Continuity
- Countability and Uncountability
- Foundations of the Real Numbers for Analysis
- Fundamental Trigonometric Identities
- Limits of Real Functions
- limsup, liminf, and Subsequential Limits
- Monotone Functions, Discontinuities, and Continuity Sets
- Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness
- Power Series and Real-Analytic Functions
- Properties of the Integral and the Working FTC
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Sequences and Series of Functions; Uniform Convergence
- Series: Convergence and the Nonnegative Tests
- Sine, Cosine, and the Definition of Pi
- Suprema and Infima
- The Derivative and the Mean Value Theorems
- The Riemann Integral: Definition and Integrability
- Topology of ℝ
Set Theory
2 · Logical flowchart
3 · Items
Example
Addition and half-angle identities compute the sine, cosine, and tangent of π/12
Example
Morrie's law: cos(π/9)cos(2π/9)cos(4π/9)=1/8
Example
Exact sine and cosine values at π/10, π/5, and 2π/5
Example
T₀ through T₄ and U₀ through U₃ from the Chebyshev recurrences
Counterexample
sin(3π/2)=-1 shows that the positive square root is not an unconditional half-angle formula
Counterexample