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The General Solution of Trigonometric Equations

The basic trigonometric functions – sin, cos, tan – have many symmetries. All areperiodic, repeating everyor 360 degrees. In addition:

cos is symmetric aboutsoIn fact cos is symmetric aboutfor any integerso

sin is symmetric aboutandso thatand In fact sin is symmetric aboutsofor any integer

tan isperiodic soIn factfor any integer

These symmetries are illustrated below.

These symmetries allow us to write down general solutions of simple trigonometric equations.

Example: Find the general solution of the equation

The general solution is then

Example: Find the general solution of the equation

The general solution is then

Example: Find the general solution of the equation

The general solution is then

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