]> Exercise 2.7

Exercise 2.7

What are the appropriate signs for each of these functions in the different quadrants?


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.