What operating sign does tangent have in Quadrant 4 of the unit circle?

What operating sign does tangent have in Quadrant 4 of the unit circle?

• A. Positive
• B. Negative
• C. Zero
• D. Undefined

Answer: (B)

In Quadrant IV of the unit circle, the x-coordinates are positive while the y-coordinates are negative. The tangent of an angle is defined as the ratio of the y-coordinate to the x-coordinate (tan(θ) = y/x). Since the y-coordinate is negative and the x-coordinate is positive in this quadrant, the result of the tangent will also be negative. Therefore, the correct answer reflects that the tangent function has a negative value when evaluated at angles located in Quadrant IV. Understanding the signs of trigonometric functions across the four quadrants helps in determining the behavior of these functions based on the coordinates on the unit circle.

In Quadrant IV of the unit circle, the x-coordinates are positive while the y-coordinates are negative. The tangent of an angle is defined as the ratio of the y-coordinate to the x-coordinate (tan(θ) = y/x). Since the y-coordinate is negative and the x-coordinate is positive in this quadrant, the result of the tangent will also be negative.

Therefore, the correct answer reflects that the tangent function has a negative value when evaluated at angles located in Quadrant IV. Understanding the signs of trigonometric functions across the four quadrants helps in determining the behavior of these functions based on the coordinates on the unit circle.