Question

help me solve this application problem?!!!!

Answer 1

\[\sin \theta=\frac{ 1 }{ 3 }, 0<\theta<\frac{ \pi }{ 2 }\]

Answer 2

\[\sin 2\theta \cos2\theta and \tan2\]

Answer 3

\[\tan2\theta \]

Answer 4

after that i get stuck :/

Answer 5

Try reaching out to a moderator or ambassador. c:

Answer 6

-_-

Answer 7

It seems to me like you might need to use some double angle formulas. Assuming you want to find \(\sin(2\theta)\), \(\cos(2\theta)\), and \(\tan(2\theta)\) correct?

Answer 8

yes i know that so far i only solved the one for cos2(theta)

Answer 9

Do you remember what the double angle formulas are?

Answer 10

In particular for \(\sin\) and \(\cos\)?

Answer 11

yes i do :P

Answer 12

Excellent. So can you quickly type them out (for sine and cosine)?

Answer 13

\[2\sin alphacos\]

Answer 14

\[\cos^2\alpha-\sin^2\alpha \]

Answer 15

\[\frac{ 2\tan \alpha }{1-\tan^2\alpha }\]

Answer 16

Those look perfect. Now before we go any further, you're triangle doesn't look right to me. It should be more likeUsing this, what is \(\cos(\alpha)\)?

Answer 17

sorry my cursor is being dumb

Answer 18

\[{\frac{ \sqrt{8}}{ 3 }}\]

Answer 19

so can we solve for sin first?

Answer 20

Right. Now you have \(\cos(\theta)\) and \(\sin(\theta)\). These are all you need to find the double angles using the formulas you were given.

Answer 21

\[\frac{ 2 }{ 1 }x \frac{ 1 }{ 3 }(\frac{ \sqrt{8} }{ 3 }\]

Answer 22

is this right ?

Answer 23

That looks alright, assuming the x is supposed multiplication. It'll simplify to\[\frac{2\sqrt{8}}{9}=\frac{4\sqrt{2}}{9}\]

Answer 24

so wait you just take out the 2 out of the 8?

Answer 25

Well, \(\sqrt{8}=2\sqrt{2}\). So I just simplified as much as I could.

Answer 26

oh alright and i just need tan

Answer 27

do we just do sin over cos of the values that we have?

Answer 28

is tan \[\frac{ \sqrt{8}}{ 8 }\]?

Answer 29

Sorry, been busy dealing with some trolls.

We can't quite jump there yet. We need to find \(\cos(2\theta)\) first. What did you get for that?

Answer 30

i got \[\frac{ 7 }{ 9 }\]

Answer 31

Right again. So then we have\[\tan(2\theta)=\frac{\sin(2\theta)}{\cos(2\theta)}\]

Answer 32

so is it 2 x \[\frac{\sqrt{8} }{ 8 }\]

Answer 33

\[1-\frac{ \sqrt{8} }{ 8 }^2\]

Answer 34

That doesn't seem right to me. It should be\[\frac{4\sqrt{2}/9}{7/9}\]The 9's will cancel out, and you'll be left with\[\frac{4\sqrt2}{7}\]

Answer 35

so we use the sin and cosine of the ones we good for the double angle?

Answer 36

did you use the tan formula?

Answer 37

are you still there?