Question

Find the exact value of each of the other five trig functions (besides the function tan) for the angle x - without finding x - given that the terminal side of x is in quadrant 2 an tan(x)=-3

Answer 1

OK so this is how i started working this one out... and I think one of my first steps is wrong.

Answer 2

tan= r/b ...therefore if given tan(x)=-3, then expressed in another way, tan=-3/1

Answer 3

aww crap... i mean... tan=b/a ... but i am still not figuring this out

Answer 4

what is 'r' the radius?.
If you have a triangle tan is b / a, where a is the 'x axis' leg and b is the 'y axis' leg

Answer 5

you can find sin and cos with this information. You know r = ?

Answer 6

Yes, r=sqrt10, this is confirmed in math book answer

Answer 7

yes, so you have all the info to find sin and cos (and the rest)

Answer 8

or it could be 3 and -1, either would work.

Answer 9

If in trig function, tan= b/a, then which is a and which is b?

Answer 10

if it can be either, than how can i know for example, what to put in sin, if sin = b/r

Answer 11

or in cotangent, when cotangent = a/b

Answer 12

how would i know what to put where in cotangent

Answer 13

BTW jkristia, I realize i suck at this and am asking a lot of questions, I appreciate your help so much.

Answer 14

hmm, I couldnt see the image once I drew it.
in this case the angle is the left angle (where r and a meet). In this case your trig functions refer to that one angle.
so tan = b/a
sin = b / r
cos = a / r

All related to that one angle. If you chose the top angle (where b and r meet) then your trigs are swapped
tan = a / b,
sin = a / r
cos = b / r

Answer 15

so if you know tan is -3, then you know that one of the leg is 3 (or - 3) and the other left is -1 (or 1), or any other values which gives the ratio -3

Answer 16

OK, so essentially you are proving here that if I am given tan= -3, a and b are interchangeable.

Answer 17

if you watch Khan's videos on trig, then he mention SOHKAHTOA many times.
It means

Sin = Opposite over Hypoternuse
Cos = Adjacent over Hypoternuse
Tan = Opposite over Adjacent

Answer 18

no, the sign is, but not the values. The ratio of a/b must be -3.

Answer 19

ok so for example, if I tried to answer this question, I could say that sin= 1/sqrt10 or sin=3/sqrt10, and either would be right?

Answer 20

In your case you are refering to two different angles.

You should pick one angle only. If you have tan = b / a = -3 and you chose b = -3 and a = 1, then you have
sin = b / r = -3 / sqrt(10)
cos = a / r = 1 / sqrt(10)

Answer 21

oh sorry yes, sorry i am dislexic ... i used b=-3, a=1

Answer 22

tan = b/a, then cot is a/b

Answer 23

I think I'm mising the a's and the b's too.
But if tan = -3, then cotan = 1/tan = -1/3

Answer 24

Well thank you for all of your 30 minutes and effort.

Answer 25

I had to restart IE, it gost stuck while writing an equation.
\[\tan = \frac{b}{a}, \cot = \frac{a}{b} = \frac{1}{\tan}\]
so what you have is correct.

Answer 26

Did it get any clearer, or did I just manage to make you even more confused?.
Just rememebr that the trig functions are for a given angle. If you pick another angle, the values will change.

Answer 27

Well... with this limited information, can you just arbitrarily pick which one will be a and b, for this one example problem?

Answer 28

no, tan is the opposite side over the adjacent side. That is the side opposite to the angle is 'b' and the side adjacent to the angle is 'a'.
So now you know which is a and which is b, then you can find r, and all the other trig functions for that same angle.
Maybe it would be good to watch the Khan videos on trigonometry, I found them very helpful.

http://www.khanacademy.org/math/trigonometry

Answer 29

because... and i promise im not being dyslexic this time... \[\tan= \frac{ b }{ a }, \] i used \[\tan(x)=\frac{ -3 }{ 1 }\]

Answer 30

how in this problem am i supposed to figure out which one is adjacent and which one is opposite?

Answer 31

Ahh - TAN is defined as opposite divided by adjacent. Since you have the -3/1 you already know that the side opposite to the angle is -3, and the side adjacent to the angle is 1

SOHCAHTOA

SOH - sin = opposite over hyp
\[\sin = \frac{-3}{\sqrt{10}}\]
CAH - cos = adjacent over hyp
\[\cos = \frac{1}{\sqrt{10}}\]
TOA - tan = opposite over adjacent
\[\tan = \frac{-3}{1}\]

Answer 32

but it never tells where the angle is...

Answer 33

found this link which shows the trigs
http://www.mathwords.com/s/sohcahtoa.htm

Answer 34

i watched the kahn academy video SOHCAHTOA 20 times

Answer 35

btw thank you

Answer 36

the angle is tan(x) = -3, so if you need to know the angle in degrees you need to take the arctan(-3) = 71.6 degress (if I got that right), but you dont need that to find the other trig values

Answer 37

oops -71.6 of course.
try tan(-71.6) and you get -3
then arctan (-3) and you get (-71.6).
Anyway - I think I'm just making you more confused.
Take a look the Khans videos, they are really good

Answer 38

oh - sorry, missed you post regarding Khan.

Answer 39

I just dont see how i am supposed to figure out which one is opposite and which one is adjacent without knowing where the angle starts off at

Answer 40

maybe this will help, it has the triangle
http://www.mathwords.com/s/sohcahtoa.htm

Answer 41

I have to run, sorry I couldnt help

Answer 42

thanks for your time.

Answer 43

If I can weigh in...
It does tell you where the angle is: in the second quadrant. Simply find the x and y values that would correspond to an angle that would appear in the second quadrant and have a value of -3.

Answer 44

Ohhh.. woops.

Answer 45

The angle could be in second and fourth quadrant, both could have a tan of -3

Answer 46

but in his problem it states that the angle is in the second quadrant. So he should only focus on the second quadrant.

Answer 47

>>side of x is in quadrant 2
argh - I missed that too

Answer 48

so - I only made him more confused. I should have read the question properly first.
Thanks

Answer 49

OK. So in summary, because tan=-3 is in quadrant 2, it must be 3/-1 because tan=y/x, and in quadrant 2, the first coordinate (x and 1) is negative, and the second coordinate (y and 3) is positive, leaving me with only one solution, that tan=-3 is = to tan=3/-1

Answer 50

correct.

Answer 51

Thank you i am so happy i figured this out you have no idea haha

Answer 52

and now you should be able to find the other trig values.