Q 18, 19 - Solving trig equations

Theory

Using trig identities, it is easy to solve trig equations like these:

Convert to polynomial

Notice in (1) the mismatch of types: in the square but without the square.

Notice in (2) the mismatch of inputs: in the cosine and in the sine.

Method: In either situation, convert to a single type and a single input using trig identities.

The result has the form of polynomial equation that can be solved.

Examples

Example (1):

Example (2):

Problems

  • Solve these equations and verify your answers.
  • If your answer is wrong, try to find your mistake and fix your solution.
  • Afterwards, study the full solution provided.

Assume that and lie in for all these problems.

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