Question

For 0°≤θ≤360°, how many roots does the equation 3sin^(2)x+2sinx-1=0 have?

let sinx=y
=> 3y^(2)+2y-1=0
y=1/3 or -1
.....

Answer 1

3y^(2) + 2y - 1 = 0
this, can be factored
(3y - 1)(y + 1) = 0
now solve for y

Answer 2

y=1/3 or -1

Answer 3

yup

Answer 4

sinx=1/3
sinx=-1

Answer 5

hmm.. for sin x = 1/3, this is not special angle in trigono. so use ur calculator to get x by take sin^-1

Answer 6

After all, you are only asked how many roots, right?
Or are they asking for specifics?

Answer 7

@RadEn sinx=1/3
x=19.471220634491

@PeterPan i also want to know what're the roots

Answer 8

Well, in that case, it doesn't look like there's much of a choice but to use calculators :)

Answer 9

one of them is 19.47

Answer 10

180-19.47=160.53 <<< is it correct?

Answer 11

Way ahead of me :)

Answer 12

any roots else?

Answer 13

sin(x) = -1

Answer 14

270

Answer 15

Those are all, I suppose. Three roots.

Answer 16

okay, thanks

Answer 17

agreed ^

Answer 18

and 0°≤θ≤360°, how many roots does the equation cos^(3)x=cosx have?

Answer 19

Do the same, but first, rearrange into
cos^3(x) - cos(x) = 0
and let y = cos(x) this time

Answer 20

y^(3)-y=0

Answer 21

Yes... and this can be factored. quite nicely, actually.

Answer 22

It factors neatly into
y(y - 1)(y + 1)

Answer 23

So what are the values for y?

Answer 24

cosx=0
cosx=1
cosx=-1

Answer 25

That's right. And these are all special, aren't they? ^.^

Answer 26

90 , 270, 0, 360, 180

Answer 27

five??

Answer 28

five roots...
I find it a bit weird that both 0 and 360 are included, aren't they essentially the same?

But yeah, you said your interval was 0°≤θ≤360°
So you're correct. And yes, five.

Answer 29

another person also confusing that 0 and 360, i think these two should be included

Answer 30

It should be safe enough. ^.^

Answer 31

For 0°≤θ≤360°, how many roots does the equation 2cos^(2)θ-5sinθ-4=0 have ?

Answer 32

Leveling up? ^_^
Why did you change cos to sin? That's not allowed :)

Answer 33

-2sin^(2)θ-5sinθ-2=0

Answer 34

ohh. okay...

Answer 35

2cos^(2)θ-5sinθ-4=0
2(1-sin^(2)θ)-5sinθ-4=0

Answer 36

Then the answer is zero roots :D

Answer 37

sinx=-2 or -0.5

Answer 38

or that... I thought you said imaginary?

Answer 39

nothing, i press the calculator wrongly

Answer 40

Okay, so you've worked out that sinx = -2 or sin(x) = -0.5
What's your conclusion? :D

Answer 41

i got 150° so far..

Answer 42

Okay, just had to convince myself :D
150 is good, and there should be one more...

Answer 43

wait, no.... 150 is not good at all, you need
sin(x) = -0.5
sin(150) = 0.5

Answer 44

210?

Answer 45

Yeah, much better :)
And one more.

Answer 46

sin^(-1) -2?

Answer 47

no... uhh
one more value for x which would make
sin(x) = -0.5

NOTE: There is no value for x which would make
sin(x) = -2
sin only ranges from -1 to 1 ^.^

Answer 48

ohh, yes..

Answer 49

sinx=-0.5
x=-30
270-(-30)=300 ?

Answer 50

Most excellent ^.^

Answer 51

3 roots?

Answer 52

Only two :)

Answer 53

the two values for x which would make sin(x) = -0.5

Answer 54

ohh yes.

Answer 55

i understand the concept now :)
thank you very much

Answer 56

You're quite welcome ^.^

Answer 57

how about...

Answer 58

For 0°≤θ≤360°, how many roots does the equation tanx=2sinx have?