Hi! I need to find the range of the function y = cos(x) on the interval -pi/6<x<pi/4. Help would be appreciated!
If you want a kind of graphical intepretation of the problem then draw the goniometric circle and also an angle and an angle .
You can see that .
If then
If then
And offcourse if then
That means that
is the lower limit of the range and 1 the upper limit of the range, therefore the range is:
Cos(x) decreases, from 1 to 0, for x from 0 to . is in that range so one end point is . One way to remember that is to remember that so if a right triangle has one angle radians, the other is also. Of course, if two angles are equal, the sides opposite them are also equal. That is, we have an isosceles right triangle. If one leg has length s, so has the other and the length of the hypotenuse, c, is given by so . The cosine is "opposite side over they hypotenuse" so .