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## 5.9 Chapter summary (EMA3Y)

Presentation: 2FT2

• We can define three trigonometric ratios for right-angled triangles: sine ($$\sin$$), cosine ($$\cos$$) and tangent ($$\tan$$)

These ratios can be defined as:

• $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{r}$$
• $$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{r}$$
• $$\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{y}{x}$$
• Each of these ratios have a reciprocal: cosecant ($$\text{cosec }$$), secant ($$\sec$$) and cotangent ($$\cot$$).

These ratios can be defined as:

• $$\text{cosec } \theta = \frac{\text{hypotenuse}}{\text{opposite}} = \frac{r}{y}$$
• $$\sec \theta = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{r}{x}$$
• $$\cot \theta = \frac{\text{adjacent}}{\text{opposite}} = \frac{x}{y}$$
• We can use the principles of solving equations and the trigonometric ratios to help us solve simple trigonometric equations.

• For some special angles (0°, 30°, 45°, 60° and 90°), we can easily find the values of $$\sin$$, $$\cos$$ and $$\tan$$ without using a calculator.

• We can extend the definitions of the trigonometric ratios to any angle.