Final answer:
Trigonometric ratios have different signs across the four quadrants: all are positive in Quadrant I, sine is positive in Quadrant II, tangent is positive in Quadrant III, and cosine is positive in Quadrant IV.
Step-by-step explanation:
The trigonometric ratios - sine, cosine, and tangent, have different signs depending on which quadrant an angle is situated in. The four quadrants of the Cartesian plane are defined by the positive and negative axes of x and y, and the angle of interest is always measured from the positive x-axis moving counter-clockwise.
- In Quadrant I, all trigonometric ratios are positive.
- In Quadrant II, sine is positive, but cosine and tangent are negative.
- In Quadrant III, tangent is positive, while sine and cosine are negative.
- In Quadrant IV, cosine is positive, but sine and tangent are negative.
Understanding the sign of these ratios in each quadrant is essential for solving trigonometry problems involving angles greater than 90 degrees and less than 360 degrees.