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

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

• A. Both positive
• B. Both negative
• C. Sine positive, Tangent negative
• D. Sine negative, Tangent positive

Answer: (C)

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.

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.