Question

what is sin theta if cot theta = -7/8 in quadrant 4

Answer 1

Do you know how to start this

Answer 2

yes \[1+\cot =\]

Answer 3

csc

Answer 4

Thats an identity.

You first start by drawing a triangle that would be in Quadrant 4:

Answer 5

ok, then what?

Answer 6

Then you need to remember your Trig rules and the pythagorean theorum. These formulas are your guide, and the pythagorean theorum is the tool you will use to find out any additional information that the problem doesnt give to you:

Sin = \(\frac{ y }{ r }\)
Cos = \(\frac{ x }{ r }\)
Tan = \(\frac{ y }{ x }\)
Csc=\(\frac{ r }{ y }\)
Sec=\(\frac{ r }{ x }\)
Cot=\(\frac{ x }{ y }\)

Pythagorean Theorum:
\[x^2+y^2=r^2\]

So with the information your given in the problem you know:

Cot = \(-\frac{ 7 }{ 8 }\)

So you know that
x=7
and y = 8

But remember that y values in the 4th quadrant are negative so your values end up being

x=7
y=-8

From there just plug in.