What are the operating signs of sine and tangent in Quadrant 2 of the unit circle?

In the unit circle, the signs of the trigonometric functions are determined by the quadrant in which the angle lies. Quadrant 2 is characterized by angles ranging from 90 degrees (π/2 radians) to 180 degrees (π radians).

In this quadrant, the sine function is positive because it corresponds to the y-coordinate of points on the unit circle, which is above the x-axis in Quadrant 2. Therefore, any angle within this quadrant will yield a positive value for sine.

On the other hand, the tangent function, which is the ratio of sine to cosine (tan(θ) = sin(θ)/cos(θ)), will be negative in this quadrant. This is because the cosine function is negative in Quadrant 2 due to the x-coordinates of points on the unit circle being negative, while sine remains positive. The division of a positive value (sine) by a negative value (cosine) results in a negative value for tangent.

Thus, in Quadrant 2, sine is positive and tangent is negative, making the correct answer align with these behaviors.