Part 2/6:
Trigonometric functions are defined as ratios of the triangle's sides:
- Sine:
[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} ]
- Cosine:
[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} ]
- Tangent:
[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sin(\theta)}{\cos(\theta)} ]
This implies that tangent can be seen as the ratio of sine to cosine, which simplifies to opposite over adjacent when the hypotenuse is canceled out.
Calculating Angles Less Than 90 Degrees
When dealing with angles less than or equal to 90 degrees (or π/2 radians), the standard definitions of sine, cosine, and tangent apply directly.