Question

Write the first trigonometric function in terms of the second for θ in the given quadrant.
csc θ, cot θ; θ in quadrant III

Answer 1

missing something?

Answer 2

nope thats the problem loll
any idea?

Answer 3

you have to find csc θ =

Answer 4

yeah i see what it is asking

Answer 5

you know
\[\sin^2(\theta)+\cos^2(\theta)=1\] divide by \(\sin^2(\theta)\) to get
\[1+\cot^2(\theta)=\csc^2(\theta)\]

Answer 6

that means
\[\csc(\theta)=\pm\sqrt{1+\cot^2(\theta)}\]

Answer 7

in quadrant 3 cosecant is negative, so pick
\[\csc(\theta)=-\sqrt{1+\cot^2(\theta)}\]

Answer 8

yeah i was thinking the same but they gave csc(sine) but also cot which is tan

Answer 9

can you please explain how you got 1+cot2(θ)=csc2(θ) when you divided by sin^2theta?

Answer 10

\[\frac{\sin^2\theta}{\sin^2\theta}+\frac{\cos^2\theta}{\sin^2\theta}=\frac{1}{\sin^2 \theta}\]Now simplify that

Answer 11

The Pythagorean Identities are the original and the two you can easily get. One of then you get by dividing through by sine, the other you get by dividing through by cosine.