General Solutions of Trigonometric Equations
Because trigonometric functions are periodic, equations have infinitely many solutions expressed by general formulae in terms of an integer n.
What is General Solutions of Trigonometric Equations?
Because trigonometric functions are periodic, equations have infinitely many solutions expressed by general formulae in terms of an integer n.
Key formula / rule: sin t = sin a gives t = n*π + (-1)n a.
Key points
- Derive the general solution of a basic trigonometric equation.
- Evaluate candidate solutions and discard extraneous roots.
Common exam trap
Dividing both sides by cos t and losing the solutions where cos t = 0.
Definitions
- Term
General Solutions of Trigonometric Equations
- Meaning
Because trigonometric functions are periodic, equations have infinitely many solutions expressed by general formulae in terms of an integer n.
- Term
General Solutions of Trigonometric Equations — explanation
- Meaning
Solving reduces to a principal value plus the periodic family. Extraneous roots appear whenever squaring or dividing by a possibly zero factor is used, so verification is compulsory.
Learning objectives
Derive the general solution of a basic trigonometric equation.
Evaluate candidate solutions and discard extraneous roots.
Formulae
- Key point
sin t = sin a gives t = n*π + (-1)n a.
- Key point
cos t = cos a gives t = 2n*π +/- a.
- Key point
tan t = tan a gives t = n*π + a.
Prerequisites
MAT-U5-TR-T1-S1-C1
Common mistakes
Dividing both sides by cos t and losing the solutions where cos t = 0.
Reporting only the principal value when a general solution is required.
Keywords
General
Solutions
Trigonometric
Equations
Practice preview
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