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NSWMaths AdvancedQuick questions

Year 12: Trigonometric Functions

Quick questions on Solving trigonometric equations: principal values, multiple angles and quadratics in sine and cosine

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is finding all solutions on the unit circle, stage by stage?
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The whole procedure for a basic equation is best seen as a build-up on the unit circle. Take sin⁡x=12\sin x = \frac{1}{2} on 0≤x≤2π0 \le x \le 2\pi. Work through it in four stages.
What are reducing with identities?
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If an equation mixes trig functions, use identities to reduce to one. Common moves:
What is wrong quadrants from the wrong identity?
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If sin⁡x<0\sin x < 0 and you "find" xx in Q1 or Q2, you have the wrong sign. Always use the quadrant rule (ASTC) to place the solution.

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