Chapter 12.3, Problem 73WE

To determine

Write given in terms of $\sin \theta$ and $\cos \theta$ .

Answer to Problem 73WE

  $\cos \left({180}^{\circ }+\theta \right)=-\cos \theta$

Explanation of Solution

Given information :

  $\cos \left({180}^{\circ }+\theta \right)$

Here we shall use a trigonometric identity,

  $\cos \left(a+b\right)=\cos a\cos b-\sin a\sin b$

Now we shall solve,

  $\cos \left({180}^{\circ }+\theta \right)=\cos {180}^{\circ }\cos \theta -\sin {180}^{\circ }\sin \theta$

  $\left(\sin {180}^{\circ }=0,\cos {180}^{\circ }=-1\right)$

  $\cos {180}^{\circ }\cos \theta -\sin {180}^{\circ }\sin \theta =-\cos \theta -0$

Hence we can say that $\cos \left({180}^{\circ }+\theta \right)=-\cos \theta$