Question

a

Answer 1

I think you can use calculator for solving this problem

Answer 2

2sin(2θ)=0.92,
sin(2θ)=0.92/2
2θ = 27.387
θ = 13.6935
180°≤θ≤360°
θ in quad. III = 180° +θ = 193.6935
θ in quad IV = 360 -θ = 346.3065
Do the checking,
2sin(2θ) = 2sin 2(193.6935) = 0.92
2sin(2θ) = 2sin2(346.3065) = -0.92 (rejected)
So θ = 193.6935
Not sure if it works, i just guess..

Answer 3

I'm with Callisto :)

Answer 4

sin(2θ)=0.92/2
sin(2θ)= 0.46
(2θ) = sin^-1 (0.46)
(2θ) = 27.387

Answer 5

you should also note that i miss out 'sin' to get 27.387 just now

Answer 6

I got exact the result!

Answer 7

2sin(2θ)=0.92
:. sin(2θ)=0.46
:.2θ=0.477995 rad
:.θ=0.238997599 rad

Answer 8

:θ=0.238997599 rad is also 13.69355375 degree

Answer 9

@duy11nv But 180°≤θ≤360°

Answer 10

I get it now, thank you :D

Answer 11

@callisto you right

Answer 12

Nah.. convert the answer in degree into rad if you need

Answer 13

But how do you get the second answer now?

Answer 14

\[\pi\] radian ~ \[180^{0}\]
so x radian ~ \[(x: \pi)*180\]

Answer 15

I know that the second answer is 4.4705716...rad, and 256.1448889753...°

Answer 16

But how?

Answer 17

Using properties of sine fuction, that sin(Pi-x)=sin(x) or sin(180-x)=sin(x)

Answer 18

you're to have two anwsers for theta

Answer 19

270 - θ ?!

Answer 20

But how do I write that down like you did before " θ in quad. III = 180° +θ = 193.6935"

Answer 21

@ricnus, don't you have the answer so you can know which solutions are correct ?

Answer 22

I know what the solutions are only because of a calculator, but I need to know how to do this

Answer 23

you need to expand the equation to give a quadratic expression
\[2\sin(2\theta) = 4\sin \theta \cos \theta\]

Answer 24

i suggest you use tan theta

Answer 25

\[4\sin \theta \cos \theta = (4\tan \theta)/(1+\tan ^{2}\theta)\] @ ricnus

Answer 26

the values for theta are

pi + 0.2389... and 2pi - 0.2389.....

this will give 2theta = 2(pi + 0.2389...) and 2(2pi - 0.2389...)

which woll put the angles in the 1st and 2nd quadrants

sin is positive in those quadrants and

will result in the fact that

\[2\sin(2\theta) =0.92\]

the domain restriction is on theta and not 2 theta...

Answer 27

\[\therefore Tan(\theta) =y\]

Answer 28

@EarthCitizen and how does (4tanθ)/(1+tan^2(θ)) help, I am so confused by this

Answer 29

@ricnus it's an identity, didn't you do that in class before doing this question ?

Answer 30

The answer by campbell_st is correct. I suggest you focus on his explanation.

Answer 31

you should have\[0.92y ^{2}-4y+0.92=0\]

Answer 32

Yes I know that, that is an identity, but how does it help it?

Answer 33

@campbell_st But for this: 2(2pi - 0.2389...), i got a -ve result, ...

Answer 34

Oh, making it into a quadratic :D

Answer 35

solve for y, by using quadratic formula

Answer 36

@ricnus yep

Answer 37

Sorry, I understood how you got the identity, but I only just realised what it could be used for :D

Answer 38

yh, no p! the equation should give you y = 4.10417 or 0.243655

Answer 39

recall, \[y = ta n \theta\]

Answer 40

you use that to find theta by taking the inverse of tan

Answer 41

Hence,
\[ta n \theta = 4.10417, ta n \theta=0.243655\]

Answer 42

solve for theta

Answer 43

\[\theta = 76.31^{o}, 14^{o}\]

Answer 44

no, it has to be within the range of 180 and 360

Answer 45

what are the answers in your text book ?