is the cos x<0 in quad 2 and 3?
yes
scroll down to "Panel 8" on this page
http://www.physics.uoguelph.ca/tutorials/trig/trigonom2.html
Yes, the cosine function (cos(x)) is negative in Quadrant 2 and Quadrant 3. To understand why, let's consider the unit circle.
The unit circle is a circle with a radius of 1 unit centered at the origin (0, 0) on a coordinate plane. When we measure the angle counterclockwise from the positive x-axis to a point on the unit circle, we can determine the values of trigonometric functions at that angle.
In Quadrant 2, the x-coordinate is negative while the y-coordinate is positive. Since cosine is defined as the ratio of the adjacent side to the hypotenuse, it is represented by the x-coordinate of the point on the unit circle. Therefore, in Quadrant 2, the cosine value is negative.
In Quadrant 3, both the x-coordinate and the y-coordinate are negative. Since cosine is defined as the ratio of the adjacent side to the hypotenuse, it remains the x-coordinate of the point on the unit circle, which is negative in this case. Hence, the cosine value is also negative in Quadrant 3.
To summarize, the cosine function is negative in Quadrant 2 and Quadrant 3.