Question

can i please get help with this, i dont know how to solve it

Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5

Answer 1

there is a formula for sin(2x)

Answer 2

do you know what it is?

Answer 3

i dont think so

Answer 4

sin(2x) = 2sin(x)cos(x)

Answer 5

Equation: 7 sin2x - 14 sin x + 2 = -5
move 2 to the other side to get?

Answer 6

@q12157: Very nice start, very helpful. Be certain to let mabitrix find his or her own answer(s), with your guidance.

Answer 7

7 sin2x -14 sinx = -3

Answer 8

now plug in the formula for sin(2x) to get?

Answer 9

also its not -3 its -7

Answer 10

since you are subtracting 2 on both sides

Answer 11

7 2sin(x)cos(x) -14 sinx = -7 ?

Answer 12

7 2sin(x)cos(x) is the same as 14sin(x)cos(x) right?

Answer 13

yes

Answer 14

aren't i supposed to make the equation =0?

Answer 15

question... is it sin(2x) or is it sin^2(x) for the problem...

Answer 16

if its sin^2(x)...its a totally different process lol

Answer 17

oh it's sin^2(x)

Answer 18

lol...
7 sin^2(x) - 14 sin x + 2 = -5

move -5 to other side to get:

7 sin^2(x) - 14 sin x + 7 = 0

Divide everything by 7 to get

sin^2(x) - 2sin x + 1 = 0

Correct?

Answer 19

yea i get it better now

Answer 20

The trick here is now to take a variable such as B and set that equal to sin(x)
so B=sin(x)

Thus the equation becomes

B^2-2B+1=0

Answer 21

Do you know how to factor this?

Answer 22

The equation becomes:
(B-1)*(B-1)=0

Answer 23

Have you learnt multiplicity yet?

Answer 24

so so i do
(sinx - 1)(sinx -1)=0 ?

Answer 25

Yep

Answer 26

so what does sin(x)=?

Answer 27

but why is it -1 in the parenthesis?

Answer 28

sinx = 1

Answer 29

its (sin(x) - 1)(sin(x) -1)=0

Answer 30

and yep

Answer 31

since sinx=1 what does x=?

Answer 32

do i do sin^-1 (1)? and thats equal pi/2?

Answer 33

yep! except theres a catch...

Answer 34

The question asks to find "all solutions"

Answer 35

thus (pi/2)+2pi is also a solution, cause if you go all the way around the circle it still causes sin(x) to equal 1.

Thus the real answer is:

(pi/2)+2pi*k where k is any positive or negative integer constant

Answer 36

(yes you'd have to write that full answer down on your hw to receive full credit)

Answer 37

oh i understand, thank you for your help!