Final answer:
In quadrant three, both the sine and cosine ratios are negative. However, only cosine is the trigonometric ratio that is specifically negative when an angle's terminal side passes through a point in this quadrant.
Step-by-step explanation:
The trigonometric ratio that is negative in quadrant three where the terminal side of an angle theta passes through the point (-3,-3) can be determined by considering the signs of the coordinates in this quadrant. In quadrant three, both the x-coordinate (adjacent) and y-coordinate (opposite) are negative, while the hypotenuse of a right triangle is always positive. According to the definitions of trigonometric ratios:
- Sine (θ) = opposite/hypotenuse
- Cosine (θ) = adjacent/hypotenuse
- Tangent (θ) = opposite/adjacent
Since both the opposite and adjacent sides are negative in quadrant three, the sine and cosine ratios would be negative as they involve a negative number divided by a positive number (the hypotenuse). However, the tangent ratio would be positive since it involves dividing two negative numbers (opposite and adjacent). Therefore, both the sine (sin) and cosine (cos) are negative in quadrant three, but since the question asks for only one ratio, the correct answer is
B) Cosine