



 
So I've gotten this far: \[\frac{\mbox{delta(y)}}{\mbox{delta(x)}} = \frac{\cot\left(\frac{7 \pi}{4}\right)\cot\left(\frac{5 \pi}{4}\right)}{\frac{7 \pi}{4}  \frac{5 \pi}{4}}\] I'm working through the example with the software, so I'm supposed to simplify the numerator. \[\frac{\mbox{delta(y)}}{\mbox{delta(x)}} = \frac{\cot\left(\frac{7 \pi}{4}\right)\cot\left(\frac{5 \pi}{4}\right)}{\frac{7 \pi}{4}  \frac{5 \pi}{4}} =\frac{ \cot\left(\frac{\pi}{2}\right)}{\frac{\pi}{2}} = \frac{1/2}{\pi/2}\] But they have: \[\frac{\mbox{delta(y)}}{\mbox{delta(x)}} = \frac{2}{\pi/2}\] And I have no idea how they got it. Can you help me? Hi Brianna, The problem is that \[\cot(A)  \cot(B) \neq \cot(A  B).\] You need to think about $\cot(7 \pi/2)$ and $\cot(5 \pi/2)$ separately. I would do so using a circle diagram. Since $\frac{5}{4} = 1 /frac{1}{4}$ the counterclockwise angle from the positive Xaxis to the line segment joining the center of the circle and $Q$ measures $\frac{5 \pi}{4}$ radians. From the diagram what do you know about the sine and cosine of this angle? What is the cotangent of this angle? Draw the angle which measures $\frac{5 \pi}{4}$ radians on this diagram and ask the same questions. I hope this helps,  


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 