Mathematics (AS)·Trigonometry · NSSCAS 2.3.4
The form R sin(θ ± α)
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In this lesson you'll learn how a sine wave added to a cosine wave is really one single sine wave, just shifted along. You'll be able to rewrite a sinθ + b cosθ in the form R sin(θ ± α) with R positive and α between 0° and 90°. You'll use that form to solve trig equations and to read off maximum and minimum values with the angles where they happen. Calm, step by step, with two full worked examples.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.3.4):
- Express a sinθ + b cosθ, a sinθ − b cosθ and a cosθ − b sinθ in the forms R sin(θ ± α) and R cos(θ ± α), where R > 0 and 0° < α < 90°.
- Use the R form to solve trigonometric equations and to find maximum and minimum values, stating the angle at which each occurs.
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