5.13 Solve trigonometric equations

AQA Edexcel OCR A OCR B (MEI)
Common things to watch out for when solving trignometric equations:

  • Is it a "disguised" quadratic equation?

  • Are your answers valid for the range given in the question?

  • Are your answers in the correct form (radians vs degrees)?

  • Have you missed any angles? Remember that every time you do \(\arcsin{x}\), \(\arccos{x}\) or \(\arctan{x}\), there is another angle.

  • For \(y = \arcsin{x}\), the other angle is \((180\degree-y)\).

  • For \(y = \arccos{x}\), the other angle is \((360\degree-y)\).

  • For \(y=\arctan{x}\), the other angle is \((180\degree+y)\).

  • Check your answers on a graphic calculator!
Important
Solving trigonometric equations

For \(y = \arcsin{x}\), the other angle is \((180\degree-y)\).
For \(y = \arccos{x}\), the other angle is \((360\degree-y)\).
For \(y= \arctan{x}\), the other angle is \((180\degree+y)\).
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