How do you find the quadrants in which the terminal side of #theta# must lie given #sintheta# is negative and #tan theta# is positive?

1 Answer
Mar 5, 2018

Answer:

III

Explanation:

We know:

#sintheta="opposite"/"hypotenuse"#

The hypotenuse is always positive by definition:

i.e. The square on the hypotenuse is equal to the sum of the squares of the other two sides. The square of a number is always positive.

If #sintheta# is negative, then the opposite side must be negative.

#tantheta= "opposite"/"adjacent"#

If this is positive then the adjacent side must be negative.

i.e

#tantheta=(-"opposite")/-"adjacent"="opposite"/"adjacent"#

So we have both negative x values and negative y values. This must therefore be in the III quadrant.