Home  18.013A  Chapter 2  Section 2.2 


What are the appropriate signs for each of these functions in the different quadrants?
Solution:
All these functions are positive in the first quadrant. Cosine is an even function of $x$ and sine and tangent are odd functions. Therefore cosine is positive in the fourth quadrant while sine and tangent are negative there.
Since $\mathrm{cos}x=\mathrm{sin}(\frac{\pi}{2}x),\mathrm{cos}x$ is negative in the second quadrant, (for $x$ between $\frac{\pi}{2}$ and $\pi $ ) and since it is an even function it is negative in the third quadrant as well.
The relations between cosine and sine and tangent and the two yields the results:
Sine: positive in the first and second quadrants otherwise negative.
Cosine: positive in the first and fourth quadrants, otherwise negative.
Tangent: positive in the first and third quadrant negative in the others.
