If $cos (θ) = \frac{2}{3}$ $Cos(theta)= 2/3$ then what is $cos (θ + π)$ $cos(theta + pi)$ ?

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Answer 1 · 2016-10-04T15:53:22

$cos (θ + π) = - \frac{2}{3}$ $cos(theta+pi)=-2/3$

Use the formula cos(A+B)=cosAcosB-sinAsinB.So
$cos (θ + π) = cos θ cos π - sin θ sin π$ $cos(theta+pi)=cos theta cos pi -sin theta sin pi$

$= \frac{2}{3} (- 1) - sin θ (0)$ $=2/3 (-1)-sin theta (0)$

Note that we can find the sin of theta from the given ratio but since sine of pi is 0 we don't have to bother finding it.

$= - \frac{2}{3} - 0$ $=-2/3 -0$

$= - \frac{2}{3}$ $=-2/3$

If cos(θ)=23Cos(theta)= 2/3 then what is cos(θ+π)cos(theta + pi)?