Chapter 5.2, Problem 56E

To determine

Write the first expression in terms of second if the terminal point determined by t.

Answer to Problem 56E

  ${\cos }^{2}t=\sqrt{1-{\sin }^{2}t}$

Explanation of Solution

Given information:

  $\cos t,\sin t;QuadrantIV$

Formula used:

  ${\sin }^2\theta +{\cos }^2\theta =1$

Now in formula ${\sin }^2\theta +{\cos }^2\theta =1$ putting value of $\theta =t$

  $\begin{array}{l}{\sin }^{2}t+{\cos }^{2}t=1\\ {\cos }^{2}t=1-{\sin }^{2}t\\ \cos t=\pm \sqrt{1-{\sin }^{2}t}\end{array}$

  $\cos \theta$ is positive in $IV$ quadrants therefore,

  $\boxed{\cos t=\sqrt{1-{\sin }^{2}t}}$