Key Concepts:
- The three primary trigonometric ratios for right triangles:
- (\sin(\theta) = \frac{opposite}{hypotenuse})
- (\cos(\theta) = \frac{adjacent}{hypotenuse})
- (\tan(\theta) = \frac{opposite}{adjacent})
- Trigonometric identities:
- (\sin A = \cos(90^\circ - A), \cos A = \sin(90^\circ - A))
- (\tan A = \frac{\sin A}{\cos A})
- (\sin^{2}x + \cos^{2}x = 1)
Skills Covered:
- Calculating sin, cos, and tan for an angle given side lengths or other trigonometric ratios.
- Finding a missing side length of a right triangle using trigonometric ratios.
Example Problems:
- In right triangle (ABC), (C) is (90°), (AB = 29), (BC = 21). Find (sin A).
- If (cos x = \frac{24}{25}), calculate (sin x).