Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

is that \(7\sin^2 x\) ?

Answer 2

is the question correct?

Answer 3

Yes it is (7sin^2x)

Answer 4

add 5 both sides

Answer 5

then divide 7

Answer 6

Then, substitute sin x = t, solve the quadratic.
Check whether the solutions lie in the range of sine fn.

Answer 7

To get sin^2x-2sinx+1?
Ok then to solve the quadratic I would make it
(sin +2)(sin-1)

Answer 8

u shoudl get

(sinx -1)^2

Answer 9

check once

Answer 10

Oh ok I see. . .
Where do i go from there?

Answer 11

(sinx -1)^2 = 0

Answer 12

solve for sinx, then solve x

Answer 13

What would be my first step?

Answer 14

take square root

(sinx -1)^2 = 0

sinx-1 = 0

Answer 15

sinx = 1

Answer 16

Wow that's great. I need to find all of the solutions now. How would I go about that?

Answer 17

when does sinx equals 1 ?

Answer 18

when x = pi/2 right ?

Answer 19

and since sin period is 2pi, for every 2pi, it gets the same value

Answer 20

Yes. Oh ok I like where this is going. I can find the other solutions knowing pi/2.

Answer 21

so 2pi/3, 4pi/3, 5pi/3

Answer 22

good :)

it wud be simply

\(\pi/2 + 2n \pi\)

Answer 23

wait no no no

Answer 24

n is any integer

Answer 25

ha

Answer 26

OK thank you so much

Answer 27

np :)