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Mathematics 16 Online
OpenStudy (anonymous):

question will be attached plz help if you can :)

OpenStudy (anonymous):

OpenStudy (anonymous):

Which question?

OpenStudy (callisto):

@SantanaG Can you clearly specify which question(s) you need help?

OpenStudy (anonymous):

any @finaiized and @Callisto

OpenStudy (anonymous):

i dont understand how to do any of the problems so i will take any help plz

OpenStudy (anonymous):

The first step is to make sure each question uses the same trigonometric ratio.

OpenStudy (anonymous):

I will do 10. \[-\sin^2x=2\cos x-2\] We want the same trigonometric ratios. So use the Pythagorean identity to convert the \(-\sin^2x\) to \(\cos^2x-1\) \[\cos^2x-1=2\cos x-2\] \[\cos^2x-2\cos x+1=0\] Hopefully you can solve the remaining bit.

OpenStudy (anonymous):

the glass steagall act regulated act regulated he stock market t or f

OpenStudy (anonymous):

@ilovejake224 ask that in the history section

OpenStudy (callisto):

Alright, then I do 11 \[2sin(2x) -2sinx + 2\sqrt3cosx -\sqrt3 =0\]\[4sinxcosx -2sinx + 2\sqrt3cosx -\sqrt3 =0\]\[2sinx(2cosx -1) + \sqrt3(2cosx -1) =0\]\[(2sinx+\sqrt3)(2cosx -1) =0\]\[(2sinx+\sqrt3)=0 \ or \ (2cosx -1) =0\] I think you can solve it!

OpenStudy (callisto):

For 12, csc(4x) -2=0 \[\frac{1}{sin4x} =2\]\[sin4x =\frac{1}{2}\] Now, you can solve it o.o...

OpenStudy (callisto):

For 13, \[cos^2(2x)-sin^2(2x) =0\]\[cos[2(2x)] =0\]\[cos(4x) =0\] Your turn to work it out!

OpenStudy (anonymous):

or 11. x=0 or x=1/396 pi)

OpenStudy (anonymous):

and 10.x=2pi?

OpenStudy (callisto):

For the last one sin2x = sinx 2sinxcosx =sinx 2cosx = 1 What's next?

OpenStudy (anonymous):

hold on im still on 12 lol :3

OpenStudy (callisto):

11 => no

OpenStudy (anonymous):

12. x=pi/24 ?

OpenStudy (callisto):

10 => yes, but you've missed another solution..

OpenStudy (anonymous):

11. x=0 and x=1/3 (6pi)

OpenStudy (anonymous):

@Callisto - Sorry for wasting your effort when you were doing 10! :(

OpenStudy (callisto):

12. => yes, but you've missed another solution (in quad. II)

OpenStudy (callisto):

@finaiized Never mind :)

OpenStudy (callisto):

11=> no

OpenStudy (anonymous):

idk what to do then for 11. sorry

OpenStudy (callisto):

Consider, \[2sinx+\sqrt3 =0\]\[sinx=-\frac{\sqrt3}{2}\] Solve x Consider \[2cosx-1=0\]\[cosx=\frac{1}{2}\]Solve x Plug in the answers you've got into the equation again, reject if it doesn't make sense :)

OpenStudy (anonymous):

For the above, make sure you recognize that they are special angles. This is how you can solve exactly. Also watch the negatives to check which quadrants they are in using CAST.

OpenStudy (anonymous):

ok thank you @Callisto and @finaiized

OpenStudy (callisto):

welcome :)

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