Solving Simultaneous Trigonometric Equations – ++ Prep

Solving Simultaneous Trigonometric Equations

00:00 3 marks

Consider the system of equations:

\(\sin(2\theta) + \cos(2\theta) = \sqrt{2}\)
\(\sin(2\theta) – \cos(2\theta) = 0\)

Solve for \(\theta\) in the interval \([0, 2\pi)\).

Hint Hint

Hint

Start by adding and subtracting the equations to isolate \(\sin(2\theta)\) and \(\cos(2\theta)\); then use the tangent function to solve.

Answer Answer
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Formula Booklet

Answer Answer

Complete Answer

\(\theta = \frac{\pi}{8} \text{ or } \theta = \frac{9\pi}{8}\)

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Answer Explanation Answer Explanation

Common Errors Common Errors

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