Question

The value pi/4 is a solution for the equation 3 sqrt 2 cos theta+2=-1

Answer 1

FALSE

Explanation:

`3\sqrt2\cos\theta+2=-1\\\\\text{Method 1}\\\\\text{Put}\ \theta=(\pi)/(4)\ \text{to the equation and check the equality:}\\\\\cos(\pi)/(4)=(\sqrt2)/(2)\\\\L_s=3\sqrt2\cos(\pi)/(4)+2=3\sqrt2\left((\sqrt2)/(2)\right)+2=((3\sqrt2)(\sqrt2))/(2)+2\\\\=((3)(2))/(2)+2=3+2=5\\\\R_s=-1\\\\L_s\\eq R_s\\\\\boxed{FALSE}`

`\text{Method 2}\\\\\text{Solve the equation:}\\\\3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\\\\3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\\\\\cos\theta=-(3)/(3\sqrt2)\\\\\cos\theta=-(1)/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)\\\\\cos\theta=-(\sqrt2)/(2)\to\theta=(3\pi)/(4)+2k\pi\ \vee\ \theta=-(3\pi)/(4)+2k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\text{It's not equal to}\ (\pi)/(4)\ \text{for any value of }\ k.`