UNIT OVERVIEW

This unit builds on the basic trigonometric ratios you learned in Grade 10. You will discover how sine, cosine and tangent connect to each other through identities. You will also learn shortcuts (reduction formulae) to simplify expressions involving any angle, and methods to solve trigonometric equations.

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

• Derive and apply the quotient identity: $\tan\theta = \frac{\sin\theta}{\cos\theta}$
• Derive and apply the Pythagorean identity: $\sin^2\theta + \cos^2\theta = 1$
• Use reduction formulae to simplify expressions involving $90° \pm \theta$, $180° \pm \theta$, $360° \pm \theta$, and $-\theta$
• Determine when a trigonometric identity is valid (restrictions)
• Solve trigonometric equations and find both general and specific solutions

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