University of California, Berkeley

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Problem 29

Determining a Quadrant In Exercises 29 and 30 , determine the quadrant in which $\theta$ lies.

$$\begin{array}{l}{\text { (a) } \sin \theta<0 \text { and } \cos \theta<0} \\ {\text { (b) } \sec \theta>0 \text { and } \cot \theta<0}\end{array}$$

Answer

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## Discussion

## Video Transcript

Okay, so we're, uh, to determine which quadrant. Um, data is based on our given information. That sign of it is just go on close, innovative Dustin Doe. So the call that we have a triangle, our hypothesis is always positive. So the only values are changing is our opposite side. Which parent signs, and our Jason side, which determines coastline. So if we have that China video is left to build in, it means that our opposite side needs to be negative. And if Cole Center data is also lessons old, then it means that our nations that have to be native so we have negative over positive would give this our hypothesis so good. So if we look at our watch it now for a question, the only time or triangle has both negative opposite side and a negative adjacent side is included. Three. Because our values here are all negative for the Y axis and here are only gonna put extra. This is Quadrant three. Great. Now report be when is speaking of data Great. Indulge in code. Hanson's of data greater than don't. Well, speaking of data is one over co sign of data that has to be created and go. And we also have attended a vada Which one? Over Tangent of beta, which is a lesson. So Okay, now, looking at this if co sign of data, we said that high parties always have to be positive. So this means that our Jason side has to be, um what do we call it? A positive, discredited girl. So it's either equality in one or Cordiant's for based on based on the destruction here. Another look at cocaine to the data. We said that coach and innovate A has to be lesson, though, but that's one over Canada data intendant of data is opposite over Jason. We set that are Jason Side because of co sign, um, it has to be grated girl are just inside is actually grated. And so So the only thing left is, uh, our opposite side news. Satisfied? If you're fixing over here since Jason, it's positive. Opposite must be negative. In order to have one of the candidate of which is close energy, they don't lesson Joe. So we need our opposite side, which is this angle here. Me ***, this is positive. And then our triangle, he'll be here. So we've determined that it is quiet for

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