If cos (t)= -1/5 find csc (t)?

[Anonymous]

I can't figure it out lol

[JackKerouac77]

Dude, neither can I.

Like, if the moon controls the tides and the Earth controls the moon, what controls in between?

Both? Do they share custody? Is the moon a boy if the Earth is a girl ("Mother Earth")?

So many questions I just can't... sleep.

[7heDubz]

Never got to trig, does this help?
cims.nyu.edu/.../...ions%20of%20Real%20Numbers.pdf

[Asker]

Sadly it doesn't help me, it would if there was more to the question like a triangle at least but there isn't :/

[BlueSJ]

Cos (t) = -1/5

t = cos-1(-1/5) = 1.77...

Csc (t) = 1/sin (t) = 1/sin [cos-1(-1/5)] = 1/sin (1.77...) = 1.020620726

Round it if you want.

[BlueSJ]

Sorry I have to repeat my answer:

Since cos is negative in the 2nd & 3rd quadrants, and cos (t) is negative, the angle is supposes to be in the 2nd or third quadrant, and you can get it by using the formulas: π-θ and π+θ, respectively.

Your θ is:
θ= cos-1(1/5) = 0.9800665778

Your angle, therefore, has two values:
t = π - θ = π - 0.9800665778 = 2.161526076
(2nd quadrant)
t = π + θ = π + 0.9800665778 = 4.121659231
(3rd quadrant)

So, you have 2 values for csc (t) as well:
csc (t) = 1/sin (t) = 1/sin (2.161526076) = 1.204043969
csc (t) = 1/sin (t) = 1/sin (4.121659231) = -1.204043969

[BlueSJ]

Supposed*

[BlueSJ]

Thank for the MHO. Hope this helped. ^-^

Yet, sorry, I have to correct something again lol.
The process is right, but I just need to correct the numbers.

θ= cos-1(1/5) = 1.369438406

So,
t = π - θ = π - 1.369438406 = 1.772154248
(2nd quadrant)
t = π + θ = π + 1.369438406 = 4.51103106
(3rd quadrant)

csc (t) = 1/sin (t) = 1/sin (1.772154248) = 1.020620726
csc (t) = 1/sin (t) = 1/sin (4.51103106) = -1.020620726

[Buwwy]

just draw the triangle, work out the 3rd side using pythagoras, find sin (t), and csc (t) comes straight from that. you dont even need to work out 't'
so should be -5/root (24)
i left my math brain way back in high school but that should be how you do it

[Buwwy]

dont overcomplicate things lol.
didn't really explain in detail but draw triangle in 2nd/3rd quadrant (accounts for the negative sign).
't' is the angle, 1 should be the length of the adjacent side, 5 of the hypotenuse.
pythagoras and you get root (24) for the opposite side
cosec (t) = hypotenuse/opposite (or 1/sin (t)) and there's your answer :)

[Buwwy]

oh my bad, the answer can be both positive or negative 5/root (24)
depends which quadrant you use

[BlueSJ]

Do you mean something like what I mentioned in my comment?

[Buwwy]

@BlueSJ yep, pretty much what i meant :) i just like to keep my answers simplified

[BlueSJ]

Great!! Haha and I like to make them clear. :P

[rjroy3]

First solve for t, so t= -1^cos (-1/5)
Then put the value of t into csc (t).
If you don't have a calculator for it, then

csc (t)= 1/sin (t) = 1/sin (-1^cos (-1/5))

[rjroy3]

Arc trig functions are a bitch to deal with

[Ghosty]

csc (θ) = 1/sin (θ), so you need θ first. You know how to get that at least?

[Asker]

No im actually helping a friend lol, i tried to figure it out on my own and had no idea what i was doing

[Ghosty]

Oh dear. You simply need to take the inverse function.

cos (t)= -1/5 //inverse of cos is arches

arccos (cos (t))=arccos (-1/5)
t=arccos (-1/5)

csc (t)=1/sin (t), therefore
csc (t)=1/sin (arccos (-1/5))

[Ghosty]

arccos, not arches lol. Dumb autocorrect.

[Quasmay]

Do you just want the answer or the how?

[Anonymous]

need to see the whole question

[Asker]

That is the whole question lol

[Opinion Owner]

Cos (t)= -1/5
Cos (t)= -0.2
Bring over the cos to other side and it becomes inverse cosine
t= cos-1 -0.2
t= 101.53

cos (101.53) = -0.199
round off to nearest number= -0.2