UNIT OVERVIEW

In this unit, you will learn how to work with compound angles — angles that are written as sums or differences of other angles, such as $\alpha + \beta$ or $\alpha - \beta$.

You might think that $\cos(\alpha + \beta)$ equals $\cos \alpha + \cos \beta$. This is not true. You will discover the correct formulas and learn how to use them.

These identities build on what you already know: special angle values, the CAST diagram, reduction formulae, and the Pythagorean identity.

By the end of this unit, you will be able to:

• Derive the compound angle identity for $\cos(\alpha - \beta)$ (this derivation is examinable)
• Apply compound angle identities for $\cos(\alpha \pm \beta)$ and $\sin(\alpha \pm \beta)$
• Derive and use double angle identities for $\sin 2\alpha$ and all three forms of $\cos 2\alpha$
• Solve trigonometric equations using these identities
• Prove trigonometric identities
• Calculate exact values of angles like $15°$ and $75°$

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