Question

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

Answer 1

Answer:

FALSE

Step-by-step explanation:

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

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