Text: Trigonometric equations
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Solving trigonometric equations
We can apply the above formulae to solve trigonometric equations. Example (3) Solve the equation [Equation goes here - download the original pdf to see it.] [Example goes here - download the original pdf to see it.] The substitution tan [Equation goes here - download the original pdf to see it.] The substitution [Equation goes here - download the original pdf to see it.] can be used to solve certain trigonometric equations. Firstly, we will show that the substitution v gives [Equation goes here - download the original pdf to see it.] To show this we start with the trigonometric identity [Equation goes here - download the original pdf to see it.] Substituting [Equation goes here - download the original pdf to see it.] into this gives [Equation goes here - download the original pdf to see it.] So, if we interpret x as an angle, this gives us the triangle [Diagram goes here - download the original pdf to see it.] The hypotenuse of this triangle is found by Pythagoras's Theorem [Equation goes here - download the original pdf to see it.] Hence [Diagram goes here - download the original pdf to see it.] From this we can deduce that [Equation goes here - download the original pdf to see it.] [Equation goes here - download the original pdf to see it.] Example (4Solve the equation: [Equation goes here - download the original pdf to see it.] [Example goes here - download the original pdf to see it.]
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Contents of
Text: Trigonometric equations
1 Trigonometric Equations Prerequisites
2 Solving trigonometric equations
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