Video Transcript
Determine the quadrant in which 𝜃
lies if cos of 𝜃 is greater than zero and sin of 𝜃 is less than zero.
We’re trying to consider a
coordinate grid and find which quadrant an angle would fall in. We’re told that cos of 𝜃 is
greater than zero, this means it has a positive cosine value, while the sin of 𝜃 is
less than zero, which means the sine has a negative value. One method we use for identifying
the sine and cosine values in different quadrants is the CAST diagram that looks
like this.
In the CAST diagram, we know that
in the first quadrant, all values are positive. In the second quadrant, only the
sine value is positive. In the third quadrant, only the
tangent value is positive. And in the fourth quadrant, only
cosine is positive. If we have a negative sine value
and a positive cosine value, we can eliminate quadrant one as all values must be
positive there. We can eliminate quadrant two as
sine is positive there. In quadrant three, sine is
negative, but so is cosine. And that means quadrant three will
not work. In quadrant four, cosine is
positive and sine is negative. And that means our angle 𝜃 under
these conditions must fall in the fourth quadrant.
