Question

Trig problem! Help!

Answer 1

2 sin(2x) - 1 = 0

Answer 2

sin (2x)=

Answer 3

The instructions are to solve for the principle values of x. Sorry I forgot to post that!

Answer 4

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

Answer 5

No need to go so far yet. From the problem give,
sin(2x)=1/2
OK?

Answer 6

Got that. I even moved the -1 over and had this:
2(sin x)(cos x) = 1
(sin x)(cos x)= 1/2

Answer 7

sin(2x) = 1/2, ok...

Answer 8

No, no need to break down into sinx cosx
if sin(2x)=1/2
then what is 2x=

Answer 9

I don't understand what is 2x...

Answer 10

\[2*sin(2x)-1=0\]\[2*sin(2x)=1\]\[sin(2x)=\frac{1}{2}\]\[2x=arcsin\left(\frac{1}{2}\right)\]\[x=15^o=\frac{\pi}{12}~rad~~or~~x=75^o=\frac{5\pi}{12}~rad\]

Answer 11

OK @D3xt3R gave you the answer

Answer 12

But I don't understand how 2x = arcsin. Please explain that part.

Answer 13

I really appreciate the answer, but I don't get the mechanics of it so it doesn't help me.

Answer 14

arcsin = inverse function of sin
for exemple:\[sin(x)=1\]x could be 90º, if we got \[sin(2x)=1\]x could be 45º, because 2x45º = 90º, isn't it?!
we just call arcsin the inverse funtion of sin, and we got and angle

Answer 15

How do you identify the inverse functions? Are they always denoted with a (2x) or something? How do you know when you are dealing with one, @D3xt3R

Answer 16

So sin(2x) will always mean arcsin? cos(2x) will always mean arccos? and tan(2x) will always mean arctan?

Answer 17

exactly

Answer 18

oh wow! So that's how you know you're dealing with the inverses? Very cool to know! Thank you so much!

Answer 19

Be careful.

the inverse function of sin(x) is arcsin
the inverse function of cos(x) is arccos
the inverse function of tan(x) is arctan

Answer 20

the inverse function of sin(2x) is \[\frac{arcsin}{2}\]

Answer 21

I see how I mistook what you said.

Answer 22

This is all very confusing at first.

Answer 23

If you have a problem like "What x give us sin(x)=1"

Now you have to find the value of x using inverse function

Answer 24

so if there's something other than an (x) inside the parenthesis, you're dealing with something other than just a plain old angle?

Answer 25

I know half angles, I thought maybe this was a double angle. How come it's not? I just don't understand how I am supposed to just KNOW that this isn't a double angle thing but an inverse function thing.

Answer 26

I prefere to use x inside the parenthesis, many people don't use this. they just write sinx

Answer 27

Look to my question just above, if you would, and answer it for me?

Answer 28

OH WAIT! I know it's an inverse because I have to divide by the sin function to get the 2x alone to solve for x, right?

Answer 29

yes

Answer 30

Thank you. I have another 2 trig problems that were kicking my butt...I'll post in a separate post so as to medal you for your help if you care to pop in and look at it.

Answer 31

OK, thanks. Mark me there ;)