Chapter 4.3, Problem 110E

To determine

(a)

To prove:

The two triangles OMP and ONQ are congruent.

To determine

(b)

To prove:

$Q=(-sin\theta ,cos\theta )$

To determine

(c)

To prove:

$\begin{array}{c}\cos \left(\theta +\frac{\pi }{2}\right)=-\sin \theta \\ \sin \left(\theta +\frac{\pi }{2}\right)=\cos \theta \end{array}$

To determine

(d)

To find:

$\tan \left(\theta +\frac{\pi }{2}\right),cot\left(\theta +\frac{\pi }{2}\right),\sec \left(\theta +\frac{\pi }{2}\right) \text{and } \csc \left(\theta +\frac{\pi }{2}\right)$