Find all the solutions between -2pi and 2pi of the equation - cos(theta)=-(1/sqrt2)

[Feeder24]

Hi all

I am asked to find all the solutions between -2pi and 2pi of the equation cos(theta) = -(1/sqrt2)

I have drawn the graph of cos, found where -(1/sqrt2) lies on the y-axis, drawn a line across to the line of cos, then drawn a line up to the x-axis, i have 4 solutions

I am struggling on how to show my working out for the exact point on the x-axis for all the solutions

Any help would be greatly appreciated, please ignore the top line 1/sqrt2 that was a mistake on my rough working out



also as a side note, how do i make sqrt, pi etc symbols, it would be easier to read, than always writing 2pi, sqrt2 etc

Thankyou

 

[Deleted member 4993]

Hi all

I am asked to find all the solutions between -2pi and 2pi of the equation cos(theta) = -(1/sqrt2)

I have drawn the graph of cos, found where -(1/sqrt2) lies on the y-axis, drawn a line across to the line of cos, then drawn a line up to the x-axis, i have 4 solutions

I am struggling on how to show my working out for the exact point on the x-axis for all the solutions

Any help would be greatly appreciated, please ignore the top line 1/sqrt2 that was a mistake on my rough working out



also as a side note, how do i make sqrt, pi etc symbols, it would be easier to read, than always writing 2pi, sqrt2 etc

Thankyou

cos(Θ) = -1/√2

\(\displaystyle \displaystyle{cos(\theta) \ = \ cos \left [(2n+1)\pi \pm \frac{\pi}{4} \right ]}............ n = 0,\ \pm 1,\ \pm 2,\ \pm 3......\)

\(\displaystyle \theta \ = \ (2n+1)\pi \pm \frac{\pi}{4}............ n = 0,\ \pm 1,\ \pm 2,\ \pm 3......\)

Continue.......

 

[Feeder24]

Thankyou, thats cleared it up and i have answers that are realistic and fit