Final answer:
The tangent of an angle is the ratio of the sine function to the cosine function of that angle. Thus, tanθ = sinθ/cosθ establishes the relationship between tangent and cosine.
Step-by-step explanation:
To compare the trigonometric functions tangent (tanθ) and cosine (cosθ), we can utilize the fundamental trigonometric identities. The tangent of an angle θ in a right triangle is defined as the ratio of the opposite side to the adjacent side, while the cosine of θ is the ratio of the adjacent side to the hypotenuse.
From the trigonometric identity tanθ = sinθ/cosθ, we can express tangent in terms of sine and cosine. Since sinθ = cosθ * tanθ, this implies that tanθ can be written as sinθ/cosθ, establishing the relationship between these two trigonometric functions. Therefore, tanθ can be viewed as the quotient of the sine and cosine functions of the same angle.