in which one quadrant is the cosecant negative and the secant positive.
Quadrant 4. Is this correct?
No, that answer is incorrect.
In the coordinate plane, the cosecant is negative in Quadrant 2 and Quadrant 3, while the secant is positive in Quadrant 1 and Quadrant 4.
So, the correct answer is Quadrant 2.
No, Quadrant 4 is not correct. To determine in which quadrant the cosecant is negative and the secant is positive, we need to consider the signs of the trigonometric functions in each quadrant.
In Quadrant 1 (the top right quadrant), all trigonometric functions are positive: sine, cosine, tangent, cotangent, secant, and cosecant.
In Quadrant 2 (the top left quadrant), only sine and cosecant are positive, while cosine, tangent, cotangent, secant are negative.
In Quadrant 3 (the bottom left quadrant), only tangent and cotangent are positive, while sine, cosine, secant, and cosecant are negative.
In Quadrant 4 (the bottom right quadrant), only secant and cosine are positive, while sine, tangent, cotangent, and cosecant are negative.
Therefore, in Quadrant 4, the cosecant is negative and the secant is positive, making it the correct answer to the question.