Which expression represents the relationship between sin and cos in terms of tangent?

The expression that correctly represents the relationship between sine, cosine, and tangent is given by the equation tan = sin/cos. This relationship is derived from the definitions of these trigonometric functions.

In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side (which corresponds to the sine function) to the length of the adjacent side (which corresponds to the cosine function). Therefore, when you take the sine of an angle and divide it by the cosine of the same angle, you arrive at the tangent function. This fundamental relationship is foundational in trigonometry and clearly illustrates how sine and cosine are interconnected through tangent.

Understanding this relationship plays a significant role in solving many trigonometric problems, as it allows for transforming expressions and equations involving sine and cosine into ones that involve tangent, which can often simplify the analysis or the calculations involved.