Question

PRE CALC HELP (picture attached)

Answer 1

@amistre64

Answer 2

you are to use the unit circle
do you have that handy?

Answer 3

http://www.mathsisfun.com/geometry/images/circle-unit-304560.gif
if not
you can find it in that link

Answer 4

pretend we want to solve \[\csc(\theta)=-2\]
since the unit circle is in terms of cos and sin you can choose to write csc as 1/sin
so we have
\[\frac{1}{\sin(\theta)}=-2 \text{ \implies } \sin(\theta)=\frac{-1}{2} \\ \text{ so we want \to find when the y value is -1/2 } \\ \text { and see what the corresponding } \theta \text{ is } \]
So we have y=-1/2 at theta=210 deg and 330 deg

Answer 5

but I don't understand what they are asking for

Answer 6

those answers i found are between 0 and 360 degs by the way
we could find answers in a different rotation around the circle

Answer 7

okay what about the 3 pi over 2 ?

Answer 8

cos(3pi/2)=0
sin(3pi/2)=-1

Answer 9

we can see this on the unit circle there there at 3pi/2 radians
the x tells us cosine there is 0
the y tells us sine there is -1

Answer 10

can you help me with #2?

Answer 11

R / Y for csc

Answer 12

have you done number 1?

Answer 13

they are looking for theta such that theta satifies the following
sin(theta)=-1/2 and there is between pi and 3pi/2

Answer 14

I thought it was 210 and 330

Answer 15

well 330 is not between 180 an 270 deg

Answer 16

so just 210

Answer 17

you instructions are weird
it says to answer with degs and rads
but the inequality is in terms of rads which means your answer should be in terms of radians so I know you must like the radians answer but listing the degree answer for number 1 seems weird to me since they have already picked theta to be in radians

Answer 18

you should list the answer in radians
and then write beneath it the following:
sin(theta)=-1/2 , 180 deg<theta<270 deg when theta=210 deg

Answer 19

ok thank you:)

Answer 20

can you help me with 2?

Answer 21

ok well like in the example I gave you I wrote the equation in terms of sine
try that here

Answer 22

so it would be in the 2nd quadrant

Answer 23

150?

Answer 24

yep
and since the question says write in radians
I would write the equation again and inequality in terms of radians
in the answer in radians

Answer 25

so beneath that I would write:
csc(theta)=2, pi/2<theta<pi when theta=150pi/180=15pi/18=5pi/6

Answer 26

okay I think I understand now ! thanks!

Answer 27

np do the 3rd one and write what you think here
and i will check you one more time

Answer 28

300?

Answer 29

yep

Answer 30

so then for that question beneath it I would put
tan(theta)=-sqrt(3), 3pi/2<theta<2pi when theta)=300pi/180=30pi/18=5pi/3

Answer 31

do you know why I'm doing this extra line stuff?

Answer 32

The instructions are weird.

Answer 33

It says they want it in both degrees and radians.

Answer 34

It also said find the answers within two rotations but that is impossible in the questions we have just solved.