Question

If cos t = 3/5 and 3π/2 < t < 2π, compute sin t and cot t.

Answer 1

Alright. First things first: I'm more comfortable with degrees as opposed to radians. Are you the same way?

Answer 2

I am not sure what they are asking me to find.

Answer 3

They want you to solve the sin of t and the cotangent of t.

Answer 4

The reason they gave us that scary 3pi/2 junk is to tell us in which quadrant our triangle will be.

Answer 5

Do you have about 5 minutes free to dedicate to this question?

Answer 6

i see so I would just to create a triangle and find the sin and cotangent

Answer 7

Yup. BUT.. we have to know which quadrant to make it. It's going to take about five minutes to explain it, so lemme know if you have that kind of time available.

Answer 8

I'll take that as a no, then?

Answer 9

I was following along uber...is the sin t = -4/5 ?

Answer 10

Oh. I was hoping to create a scribbla page. Just gie me like 5 minutes to help someone else with her question, and I'll get back with you.

Answer 11

Actually, I should be able to multitask. Could you meet me in here: http://www.scribblar.com/u306z82j

Answer 12

You are told that \(\cos t =\frac{3}{5}\), and that it is for values of t, between \(3 \pi/2<t<2\pi\). This means that t is an angle between these values, in the fourth quadrant (see attached picture).

Firstly, to find \(\sin t\), use the relationship (which is always true) that \[\sin^2 t + \cos^2 t = 1\] In other words \[\sin^2 t + \left(\frac{3}{5}\right)^2=1\] so we have that \[\sin^2 t = 1 - \left(\frac{9}{25}\right)=\frac{16}{25}\] so we have that \(\sin t = + \frac{4}{5}\) OR \(\sin t =- \frac{4}{5}\). This is where the values of t come in. As only those of the fourth quadrant are allowed, the sine function is negative, and so we take that \[\sin t = - \frac{4}{5}\]

Secondly, to get \(\cot t\), we can use the relationship that \[\tan \theta = \frac{\sin \theta}{\cos \theta}\] and that \(\cot \theta = \frac{1}{\tan \theta}\) so you have, \[\tan t = \frac{\sin t }{\cos t }= \frac{-4/5}{3/5}= \frac{-4}{3}\] and then \[\cot t = \frac{1}{tan t}= -\frac{3}{4}\]

Hope that helps

Answer 13

Opps here is the figure