Question

What values for theta (0 10 years ago

Answer 1

@AQ99

Answer 2

hmm...which do you think it is? c:

Answer 3

Well it's to solve for each of those equations >.<

The options for equation a are
a. pi/3, 5 pi/3
b. 2pi/3, 4pi/3
c. pi/6, 3pi/6
d. 7pi/6, 11pi/6

Answer 4

And the options for equation b are
a. pi/2, 2pi/2
b. 3pi/4, 5pi/4
c. pi/3, 5pi/3
d. 2pi/3, 4pi/3

Answer 5

>.< oomg

Answer 6

@iGreen @Hero Please please help!!

Answer 7

@iGreen @Hero

Answer 8

^^^great minds think alike

Answer 9

XD we both tagged him at the same time! :DD

Answer 10

@jim_thompson5910 help?

Answer 11

D: @Hero !!

Answer 12

the equation for part A is this right?

\[\Large 3\sin(\theta) = \sin(\theta) - 1\]

Answer 13

Yessir

Answer 14

the goal is to isolate theta

first isolate sin(theta)

how would you isolate sin(theta) ?

Answer 15

hint: let z = sin(theta)

that allows us to make substitutions to get 3z = z-1

what do you get when you solve for z ?

Answer 16

2z=-1? So z=-1/2?

Answer 17

good

Answer 18

so sin(theta) = -1/2

Answer 19

what values of theta make the equation \[\Large \sin(\theta) = -\frac{1}{2}\] true?

Answer 20

Yes

Answer 21

here's a unit circle to help answer the question

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png

locate any points that have -1/2 as a y coordinate. The corresponding angle will be a solution for theta

Answer 22

11pi/6?

Answer 23

and 7pi/6?

Answer 24

Can you help with equation b too?

Answer 25

yep 7pi/6 and 11pi/6

Answer 26

for equation b, you'll use the identity

\[\Large \tan^2(\theta) = \sec^2(\theta) - 1\]

Answer 27

Thanks so much for the help, jim. I was at a huge loss here :/ sorry I couldnt help out.

Answer 28

\[\Large \tan^2(\theta) = -\frac{3}{2}\sec(\theta)\]

\[\Large \sec^2(\theta)-1 = -\frac{3}{2}\sec(\theta)\]

\[\Large z^2-1 = -\frac{3}{2}z\]

\[\Large 2z^2-2 = -3z\]

\[\Large 2z^2+3z-2 = 0\]

On the third line I replaced every sec(theta) with z. I let z = sec(theta). From here you need to solve for z (use the quadratic formula)

Answer 29

z=-2? @jim_thompson5910

Answer 30

sorry that took a second /.\

Answer 31

you'll also find that z = 1/2, but sec(theta) = 1/2 has no solutions. So we can ignore that part.

Answer 32

yes z = -2 which leads to sec(theta) = -2 ---> cos(theta) = -1/2

Answer 33

Okay so what do I do next?

Answer 34

look for points on the unit circle that have an x coordinate of -1/2

Answer 35

since points of the unit circle have x coordinates corresponding to cos(theta)

Answer 36

2pi/3 and 4pi/3?

Answer 37

correct