Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

let sinx = t

and we get 7t^2 - 14t + 2 = -5

so what do you think comes next?

Answer 2

I'm not sure, subtract 2?

Answer 3

No. add 5 to both sides, and we get?

Answer 4

7t^2 - 14t + 7 ?

Answer 5

That's correct but it's equal to zero. So we have a quadratic equation!

what do you think the next step might be?

Answer 6

I can't seem to remember, can you help?

Answer 7

we have to simplify the equation and then solve for t

7t^2 - 14t + 7 = 0

can you see a common factor?

Answer 8

divide by 7t?

Answer 9

that's close. Try dividing by 7. Now what does that become?

Answer 10

t^2-2 = 0?

Answer 11

nice try, but not quite. Dividing everything by 7,

We get t^2 - 2t + 1 = 0 Do you follow?

Answer 12

o_O

Answer 13

Yes!

Answer 14

OK, now we have to factorise the quadratic. Any ideas?

Answer 15

I think I figured it out, t = 1 right?

Answer 16

Well done!!

So now we have t = 1
which means that sinx = 1

now we have to work out what values x can have. Any ideas?

Answer 17

1? Haha

Answer 18

Very funny :)

x = arcsin1 any ideas what that might be?

Answer 19

No sorry, this isn't really my greatest subject

Answer 20

Oh, I see. Have you tried using a calculator or google?

Answer 21

We're looking for an angle that has a sine of 1

Answer 22

Can you give me a hint?

Answer 23

OK, what is the sine of π/2 ?

Answer 24

1?

Answer 25

Yes, that's right. So that means that x = arcsin 1 = π/2

But that's not all! Do you know why?

Answer 26

No, so is 1 the answer?

Answer 27

No, the answer is x = π/2 + 2kπ where k = all integers

Answer 28

thank you!

Answer 29

Because the answer repeats every 2π

Answer 30

No problem. Glad I could help