in which one quadrant is the cosecant negative and the secant positive.
Quadrant 4. Is this correct?
To determine in which quadrant the cosecant is negative and the secant is positive, it is helpful to understand the signs of trigonometric functions in different quadrants.
In a coordinate plane divided into four quadrants, we can label them as follows:
1. Quadrant I: All trigonometric functions are positive.
2. Quadrant II: Only the sine and cosecant are positive.
3. Quadrant III: Only the tangent and cotangent are positive.
4. Quadrant IV: Only the cosine and secant are positive.
Given that the cosecant (csc) is the reciprocal of the sine and the secant (sec) is the reciprocal of the cosine, we can determine the sign of cosecant and secant based on the positive trigonometric functions in each quadrant.
In Quadrant IV, the cosine is positive, and therefore the secant is positive as well. In this quadrant, the sine is negative, and thus the cosecant is negative.
Therefore, your answer is correct. The cosecant is negative and the secant is positive in Quadrant IV.