Question

If sin x = -1/3 and x is in quadrant III. How do I find cosx, tanx, cotx, secx, and cscx? the negative sign is throwing me off.

Answer 1

Steps:

1) draw a triangle
2) sinx = opposite/hyp
so your hyp. = 3 then use this rule to find the last side:

\[c^2=x^2+y^2\]

3) cosx = adj/hyp
4) tanx = sinx/cosx
5) cotx = 1/tanx
6) secx = 1/cosx
7) cscx = 1/sin x

^_^ give it a try

Answer 2

you have y, find x :)

Answer 3

is x square root of 8?

Answer 4

yep ^_^ now all you have to do, is plug in the right sides in the following trigs :)

Answer 5

cos=- √8/3
tan =1/√8
cot=√8
sec= -3√8/8
csc = -3

are those right? I don't think they are

Answer 6

tan is wrong, tanx = sinx/cosx = (-1/sqrt(8))

sec is the inverse of cos x ^_^ and csc is the inverse of sinx :)

so secx = sqrt(8) /3

^_^

Answer 7

so is my x = -1
y = √8
r = 3

Answer 8

x = sqrt(8) , y = 1 and c = 3 ^_^

Answer 9

is y negative 1?

Answer 10

yep!

Answer 11

so is cos negative √8/3 or positive....

Answer 12

positive because x = positive and hyp = positive ^_^

Answer 13

hmm you said it's in the third Quadrant right?

Answer 14

if it is in the third quadrant then both sin x and cosx = negative and tan x = positive