Question

Find all solutions to the equation.

7 sin^2 x - 14 sin x + 2 = -5

Please help I don't understand

Answer 1

put sinx = 2,

7t^2 -14t + 2 = -5

Answer 2

its a quadratic now, factor and solve t

Answer 3

Is that a \[\large \sin2x\]

or a \[\large \sin^2x\]

Answer 4

it is sin^2 x

Answer 5

Then the above method provided by Sara works.

Answer 6

You let t = sin(x)
and it becomes \[\Large 7t^2-14t+2 = -5\]

Answer 7

but theres no t in the equation where do i get the t from??

Answer 8

It replaced sin(x) .
Just to ease solving.
Once you've solved for t, replace it with sin(x) again :)

Answer 9

Oh wow okay that sounds easy thank you :)

Answer 10

is this correct?

t = sin(x)
=>7t^2 + 14t + 2 = -5
=> 7t^2 + 14t = -7
=>7t^2 + t = -1/2
=>t^2 + t = -1/2(1/7)
=>t + t = sqrt -1/14
=>2t = sqrt -1/14(1/2)
=> t = sqrt 1/28

Answer 11

no. solving quadratic is bit different

Answer 12

oh okay i thought i just solve for t and thats it what did i do wrong

Answer 13

hey sorry u still stuck with this ?

Answer 14

if so,

sinx = t

7 sin^2 x - 14 sin x + 2 = -5

7t^2 - 14t + 2 = -5

7t^2 - 14t + 7 = 0

t^2 -2t + 1 = 0

(t-1)^2=0

t = 1


sinx = 1

x = \(\frac{\pi}{2} \pm 2n\pi\)

Answer 15

no i got this thanks guys1