If secant theta is more than 0 and cotangent theta is less than 0, what quadrant is theta in?

Just think of it in terms of signs. You know that secant theta has to be positive because it is greater than 0, and you know that cotangent is negative since it is less than 0. Use identities to get secant and cotangent into familiar terms. secant=1/cos and cot=cos/sin. We also know that cos corresponds to x values and sin corresponds to y values. Now just think of these two terms as x and y values. When will 1/x be positive and when will x/y be negative? the answer is the fourth quadrant. You move to the right wich allows x to positive and then down which allows y to be negative