]> Exercise 2.7

## Exercise 2.7

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 $cos ⁡ x = sin ⁡ ( π 2 − x ) , cos ⁡ x$ is negative in the second quadrant, (for $x$ between $π 2$ and $π$ ) 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.