Question

Help with trig

Answer 1

Given \[\tan(\theta)=-1/3\] and with θ in quadrant IV, find the exact value of sin(2θ).

Answer 2

draw a diagram and try to visualize

Answer 3

here to help if you try first!

Answer 4

are you allowed to use a calculator?

Answer 5

i don't think so!

Answer 6

hmmm....

Answer 7

sorry got back os didnt load :C

Answer 8

somehow i'm having a problem with OP as well, i can't see latex codes

Answer 9

question. So is -1/3 basically saying that 1 is the opposite and 3 is the adjacent?

Answer 10

yes

Answer 11

yes! and they give you the quadrant too

Answer 12

so sin must be negative, yes?

Answer 13

the first think you need to do is draw the triangle that represents this situation
then use the Pyathagoras theorem to find the missing side
then find sin theta and cos theta
that all will be used to find sin (2theta)

Answer 14

Pythagoras*

Answer 15

do some work, paper and pencil my dear, push yourself little more harder

Answer 16

do what i just mentioned!

Answer 17

Sorry i got kicked off again ._.

Answer 18

reply and best response if you understood!!..:)

Answer 19

okay good
-1 not 1
=======
now look for the hyp

Answer 20

sidarth did it pretty much you just need to work it also yourself to see if you got it

Answer 21

Question, How would you find the hypotonuse if they don't give us a degree of an angle

Answer 22

you use the Pythagorean theorem my dear

Answer 23

Oh 1+9=10 would be what it would work out too

Answer 24

you have to square the 10
that's the hyp

Answer 25

yes was about to say 10=c^2

Answer 26

okay now you got the missing side
what is sin (theta)

Answer 27

c=3.16

Answer 28

no just leave it as root 10

Answer 29

oh why do we wanna not want to work it out does it mess up?

Answer 30

hmm good question
because we might cancel the root later in calculation if you did decimal things would be the way we might want them to be

Answer 31

would not be*

Answer 32

Alright:p so now the triangle looks like

Answer 33

yes

Answer 34

So in order to get sin sin(theta=-1/sqrt10?

Answer 35

we need sin (2 theta)
and we know that sin (2 theta)=2sin (theta)cos(theta)
so we need to get sin (theta) and cos theta and multiply them out
and multiply the result by 2

Answer 36

and yes sin theta =-1/root10

Answer 37

so wouldn't we have to get theta alone for both cos and sin.

Answer 38

yes! see the relation between sin2theta with sintheta and cos theta

Answer 39

we have to do both and multiply them out

Answer 40

you can't get theta alone the other way you are used to! if that's what you are talking about

Answer 41

By arcsin I assume is what you are saying we can't do?

Answer 42

and besides there are asking us \[\sin 2\theta \] why bother with theta

Answer 43

yes we can't, in fact, why bother doing that
the question is not asking for theta

Answer 44

well I am confused, we have to find theta first then multiply it by 2?

Answer 45

\[\sin 2 \theta=2\sin \theta \cos \theta \]

Answer 46

no we are not gonna bother with theta at all

Answer 47

so wait i get it now

Answer 48

just find \[\cos \theta ~~and~~ \sin \theta \]
you already found sin theta

Answer 49

\[\sin(2x)=\sin(\frac{ -1 }{ \sqrt10 })\cos(\frac{ 3 }{sqrt10 })\]

Answer 50

no you don't get it!

Answer 51

Egh

Answer 52

why are you not paying attention to what i'm saying
\[\sin \theta = \frac{-1}{\sqrt{10}}\\ \cos \theta =\frac{3}{\sqrt{10}}\]
then \[\sin (2\theta )=2(\frac{-1}{\sqrt{10}})(\frac{3}{\sqrt{10}})\]