anonymous
  • anonymous
Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmate
  • mathmate
Not sure if you want to solve: \(7\sin^2(x)-14\sin(x)+2=-5\) or \(7\sin(2x)-14\sin(x)+2=-5\) In either case, factor out the common factor 7 to simplify things a little.
anonymous
  • anonymous
sorry the first one
anonymous
  • anonymous
But I can't factor out 7 because of the 2

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

phi
  • phi
first put it in standard form by adding +5 to both sides \[ 7\sin^2(x)-14\sin(x)+2=-5 \\ 7\sin^2(x)-14\sin(x)+7=0\]
Astrophysics
  • Astrophysics
You can always let sinx = x then factor normally and plug back sinx to find the solution
Astrophysics
  • Astrophysics
\[7x^2-14x+2=5\]
anonymous
  • anonymous
I'm sorry. Are you saying all the possible solutions are x=±7 x=±14 and x=±2?
phi
  • phi
\[ 7\sin^2(x)-14\sin(x)+7=0 \] divide both sides (and all terms) by 7. you get \[ \sin^2(x)-2\sin(x)+1=0 \] to avoid confusion, let \( y= \sin x \) and write this as \[ y^2 -2 y +1= 0 \] can you find the values for y ?
anonymous
  • anonymous
I'm so confused. My brother said y=(sqrt-.5)+y
phi
  • phi
you can factor y^2 -2 y + 1 =0 to get (y-1)(y-1)=0 now solve for y-1= 0
phi
  • phi
you get y=1 remember y= sin x so sin x =1 what "x" values have sin x = 1?
Astrophysics
  • Astrophysics
Letting x = sinx we get \[7x^2-14x+2=-5 \implies 7x^2-14x+7 =0\] divide both sides by 7 to simplify, we get \[x^2-2x+1=0\] factoring we \[(x-1)^2=0 \implies (x-1)(x-1) = 0\] Now we sub sinx back in to get \[(sinx-1)^2 = 0 \implies (sinx-1)(sinx-1) = 0\] so solving for just sinx -1 = 0, we get sinx = 1
anonymous
  • anonymous
So there's only one value?
phi
  • phi
sin goes forever. between 0 and 2pi (or 0 and 360 degrees) there is only pi/2 (90 degrees) but you can add 2pi to that answer and you will get another value that works people would write the answer as \[ x = \frac{\pi}{2} + k \cdot 2 \pi, \text{ k any integer}\]
anonymous
  • anonymous
Thank you so much guys!

Looking for something else?

Not the answer you are looking for? Search for more explanations.