Question

Find the x axis intercepts of the graph with equation
y= 2sin2(x+(pi/3))+1

Answer 1

x axis intercepts are when y = 0.
2sin2(x+(pi/3))+1 = 0
solve for x

Answer 2

Find values between -pi and pi

Answer 3

2sin2(x+(pi/3))+1 = 0
subtract 1
2sin2(x+(pi/3)) = -1
divide by 2
sin2(x+(pi/3)) = -1/2
Solve for x

Answer 4

Can you find the actual answers for me?

Answer 5

You should participate a little bit so you can learn. If you have doubts you can ask questions. If I just give you the answer then for every question like this you will have to ask someone to give you the answer. But if you learn you can do this by yourself next time.

Answer 6

I tried to work it out but it won't work

Answer 7

Where exactly are you having trouble?

Answer 8

I can get the values -pi/6 and 7pi/6 but I can't get the rest of the solutions

Answer 9

After that I know I still need to dived by 2 and subtract pi/3

Answer 10

The sine function is a periodic function with a period of 2*pi.
So if 7pi/6 is one solution, then 7pi/6 \(\pm n*2\pi \) are also the solutions.

Answer 11

sin2(x+π/3) = -1/2
In the interval [0,2π], sin(A) is -1/2 when A = 7π/6, 11π/6
Since sine function has a period of 2π, A = 7π/6 ± n∗2π or A = 11π/6 ± n∗2π
2(x+π/3) = 7π/6 ± n∗2π or 11π/6 ± n∗2π where n is 0, 1, 2, 3, ...
(x+π/3) = 7π/12 ± n∗π or 11π/12 ± n∗π
x = 7π/12 - π/3 ± n∗π or 11π/12 - π/3 ± n∗π
x = 7π/12 - π/3 ± n∗π or 11π/12 - π/3 ± n∗π
x = 7π/12 - 4π/12 ± n∗π or 11π/12 - 4π/12 ± n∗π
x = 3π/12 ± n∗π or 7π/12 ± n∗π
x = π/4 ± n∗π or 7π/12 ± n∗π
We are interested in the interval: [-π, π]
n = 0 gives x = π/4, 7π/12
n = 1 gives x = π/4 + π, 7π/12 + π, π/4 - π, 7π/12 - π
The first two are greater than π and hence outside the interval.
The last two solutions are: -3/4π, -5/12π

\(\Large x = -\frac {3\pi}{4}, -\frac{5\pi}{12}, \frac{\pi}{4}, \frac{7\pi}{12}\)