Question

How do you do this?
@ganeshie8 @hartnn @Hero @Luigi0210 @zepdrix @e.mccormick

Answer 1

looks there are some typoes in the question..

Answer 2

like what?

Answer 3

because my teacher gave me this worksheet to me?

Answer 4

excuse my bad grammar

Answer 5

i may be wrong, but i dont see yet how squaring `sinxcosx = 1` gives you `sin^4x - sin^2x+1=0`

Answer 6

\[\sin^2(x)\cos^2(x)=\sin^2(x)(1-\sin^2(x))\]

Answer 7

distribute

Answer 8

you get sin^2xcos^2x=1

Answer 9

Instead of this strategy to show there is no solutions there is awesome better way

Answer 10

but we can do what your teacher says

Answer 11

that becomes
\[\sin^2x(1-\sin^2x)=1\]
\[\sin^2x-\sin^4x=1\]
\[\sin^4x-\sin^2x+1=0\]

Answer 12

ok freckles

Answer 13

just for fun:
recall sin(2x)=2sin(x)cos(x)
sin(x)cos(x)=1
2sin(x)cos(x)=2
sin(2x)=2

Answer 14

ok

Answer 15

ahh nice :) ive missed that too :o

Answer 16

so what next freckles

Answer 17

To solve you quadratic in the form of sin^2(x)...
let u=sin^2(x)
solve u^2-u+1=0 for u

Answer 18

thats what i did and i got stuck...

Answer 19

And sin(2x)=2 has no solutions because the range of sin is from -1 to 1
2 is not in that range

Answer 20

so back to our problem

Answer 21

What did you notice about your discriminant?

Answer 22

the thing under the square root?

Answer 23

And I'm talking if you used the quadratic formula

Answer 24

it is \[-3\sin^4x\]

Answer 25

@freckles

Answer 26

@ganeshie8

Answer 27

\[u^2-u+1=0 \\ u=\frac{1 \pm \sqrt{1-4(1)(1)}}{2(1)}\]

Answer 28

look at the thing under the square root

Answer 29

what do you notice about it?

Answer 30

its negative?

Answer 31

imaginary number?

Answer 32

yes this shows there is no real solution

Answer 33

oh really?

Answer 34

i didn't think that was it...

Answer 35

what did you think it was?

Answer 36

i reached that point where i thought an imaginary number had no real solutions and i don't know.. but thanks a lot

Answer 37

but what does that say about the original equation?

Answer 38

well imaginary number implies the number is not real

Answer 39

It had no real solutions.