Question

Find 2 solutions for cot(θ)=-√3 what is the easiest way to find this?

Answer 1

http://mathway.com/answer.aspx?p=calg?p=cot%28SMB26%29SMB01-SMB203SMB15?p=1?p=?p=?p=?p=?p=0?p=?p=0?p=?p=

Answer 2

Im stuck at cot (θ)=1/-√3

Answer 3

click on that link

Answer 4

wwowwww thx!

Answer 5

Thank Mathway.com it helps me with some of my problems :)

Answer 6

Unit circle is every trig student's friend.

Answer 7

unit circle is boss

Answer 8

amazing u need to upgrade for it to show steps?

Answer 9

if your willing to pay for it then yeah lol

Answer 10

can u show me the unit circle way?

Answer 11

cheat sheet at paul's notes has excellent unit circle. i am not at home or i would attach it

Answer 12

Here's one...

Answer 13

yes normally with sin and cos i can find the values but not with others

Answer 14

lets rearrange he problem a little first:
\[\cot(\theta) = -\sqrt{3} \iff \tan(\theta) = -\frac{1}{\sqrt{3}}\iff \frac{\sin(\theta)}{\cos(\theta)} = -\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}\]

Answer 15

so we are looking for an angle that satisfies one of these two possibilities:
\[\sin (\theta) = \frac{1}{2}, \cos(\theta) = -\frac{\sqrt{3}}{2}\]
or
\[\sin(\theta) = -\frac{1}{2}, \cos(\theta) = \frac{\sqrt{3}}{2}\]

Answer 16

cos(theta)=1/-√3 is 1/tan=cot(theta) right?

Answer 17

Remember, sin is the y-value and cos is the x-value... find ( sqrt(3)/2, -1/2 ) or ( -sqrt(3)/2, 1/2 ) as points on the circle...

Answer 18

Or you could just remember a 1,2 sqrt 3 triangle....

Answer 19

waahh confused i meant cot(theta)=-√3 not cos

Answer 20

that is correct chelsea

Answer 21

yes in other words im lookin for what value 1/tan=-sqrt3

Answer 22

that right?

Answer 23

yes :)

Answer 24

-√3divided by 1 or other way around?

Answer 25

this aint makin nooo sensee

Answer 26

take a look at my second post to help you out.

Answer 27

i did confusing though it only makes sense to me if i say to myself what value x/y will give me -sqrt3?

Answer 28

right, the post under that says what values of x (which is cos) and y (which is sin) will give you that.

Answer 29

Chelsea - That's the way I think about it too...I first take what I am looking for (in your case cot) then convert to sin and cos..

So I know I need cos/sin which I think convert to x and y...since x = cos and y = sin

So I need x/y = -sqrt(3)

so my x will be sqrt(3)/2 and my y will be 1/2...and one will be negative
I find that on the unit circle and I'm done! :)

Answer 30

oh so those are 2 different coordinates but how did u narrow it down to just those two?

Answer 31

did u mentally think of those 2 fractions ?

Answer 32

Those fractions come from the 30-60-90 triangle rule. The sides of a 30-60-90 triangle are always in the ratio of 1:sqrt(3):2, respectively. So when it goes to the unit circle, all 30-60-90 points will have coordinate involving sqr(3)/2 and 1/2.

For instance, look at pi/6. This is 30 degrees so it's coordinates will be (sqrt(3)/2, 1/2)

Answer 33

If you have a problem involving sqrt(2), you're going to use the fractions sqrt(2)/2 and 1/2

Answer 34

ooooh that makes alot more sense up untill now i havent used any triangle methods reason why i didnt recognize those fractions.

Answer 35

thanks bender

Answer 36

my pleasure :)