Question

Solve each equation for 0 x 360 sqrt 2 cosx+1=0 please hurry

Answer 1

Answer:

$120\º \text{ and } 240\º$

or in radians:

$\frac{2\pi }{3} \text{ and } \frac{4\pi }{3}$

Step-by-step explanation:

From the way you wrote, you want to solve the equation

$\sqrt {2 \cos(x)+1}=0$ for $0 \leq x < 360\º$, or in radians $[0, 2\pi)$

$\sqrt {2 \cos(x)+1}=0$

Square both sides

$2 \cos(x) +1= 0$

$2\cos(x)=-1$

$\cos(x)=-\frac{1}{2}$

In the Unit Circle, considering one revolution (interval $[0, 2\pi)$),

the values where $\cos(x)=-\frac{1}{2}$  are in Quadrant II and III.

Once

$\cos(x)= \frac{1}{2} \text{ for } x = 60\º \text{ in the Quadrant I}$

The values where

$\cos(x)=-\frac{1}{2}$   are 120º and 240º.