Question 1186262
answers to your questions:


If sin θ is positive, and tan θ is negative, then what quadrant will you find the terminal arm?


sine is positive in quadrants 1 and 2.
tangent is negative in quadrants 2 and 4.


the common quadrant is quadrant 2.
that's your answer.


If cos β is positive, and sin β is positive, then what quadrant will you find the terminal arm?


cosine is positive in quadrant 1 and 4.
sine is positive in quadrant 1 and 2.


the common quadrant is quadrant 1.
that's your answer.


If cot α is positive, and csc α is negative, then what quadrant will you find the terminal arm?


cotangent, being the reciprocal of tangent, is positive in quadrant 1 and 3.
cosecant , being the reciprocal of sine, is negative in quadrant 3 and 4.


the common quadrant is quadrant 3.
that's your answer.


here's a reference.


<a href = "https://www.onemathematicalcat.org/Math/Precalculus_obj/trigSigns.htm" target = "_blank">https://www.onemathematicalcat.org/Math/Precalculus_obj/trigSigns.htm</a>