On the interval phi less or equal to theta less or equal to

On the interval -phi less or equal to theta less or equal to phi, the graphs of y = theta and y = cos theta intersect at 2 points. The graph of y = -cos (theta - phi/2) is a reflection of the graph of y = sin theta in the x - axis. The function y = 5 tan (2x - 3phi/2) is odd.

Solution

13) y = -cos( - /2)

==> y = -cos(-(/2 - ))

==> y = -cos(/2 - )               since cos(-x) = cosx

==> y = -sin()               since cos(/2 - ) = sin

Hence y = -cos( - /2) is the reflection of y = sin in the x axis

14) y = 5tan(2x - 3/2)

==> y = -5cot(2x)           since tan(- x) = -tanx , tan(3/2 - x) = cotx

x = -x ==> y = -5cot(2(-x))  

==> y = 5cot(2x)

as x = -x , y = -y

Hence y = 5tan(2x - 3/2) is odd function.