How do you solve $2 cos (\frac{x}{3}) + \sqrt{2} = 0$ $2cos(x/3)+sqrt2=0$ ?

Question

How do you solve $2 cos (\frac{x}{3}) + \sqrt{2} = 0$ $2cos(x/3)+sqrt2=0$ ?

1 Answer

Impact of this question

6564 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-20T04:59:05

$x = \frac{9 π}{4} + 6 k π$ $x = (9pi)/4 + 6kpi$
$x = \frac{15 π}{4} + 6 k π$ $x = (15pi)/4 + 6kpi$

Explanation:

$2 cos (\frac{x}{3}) + \sqrt{2} = 0$ $2cos (x/3) + sqrt2 = 0$
$cos (\frac{x}{3}) = - \frac{\sqrt{2}}{2}$ $cos (x/3) = -sqrt2/2$
Trig Table and unit circle -->
$\frac{x}{3} = \pm \frac{3 π}{4}$ $x/3 = +- (3pi)/4$

a. $\frac{x}{3} = \frac{3 π}{4} + 2 k π$ $x/3 = (3pi)/4 + 2kpi$
$x = 9 \frac{π}{4} + 6 k π$ $x = 9pi/4 + 6kpi$
b. $\frac{x}{3} = \frac{5 π}{4} + 2 k π$ $x/3 = (5pi)/4 + 2kpi$
(Arc $\frac{- 3 π}{4}$ $(-3pi)/4$ is co-terminal to arc $\frac{5 π}{4}$ $(5pi)/4$ )
$x = 15 \frac{π}{4} + 6 k π$ $x = 15pi/4 + 6kpi$ ,

Science

Math

Humanities

... and beyond

How do you solve $2 cos (\frac{x}{3}) + \sqrt{2} = 0$ $2cos(x/3)+sqrt2=0$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 2cos(x/3)+sqrt2=02cos(x3)+√2=02cos(x/3)+sqrt2=0?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $2 cos (\frac{x}{3}) + \sqrt{2} = 0$ $2cos(x/3)+sqrt2=0$ ?