Question

given that csc(theta)=7 and theta lies in the second quadrant, find

Tan(90degrees-theta)

Answer 1

does it help to know that \(\tan(90-x)=\cos(x)\)?

Answer 2

that is wrong sorry,
\[\tan(90-x)=\cot(x)\] is what i meant to write

Answer 3

so the job is to find \(\cot(x)\) knowing \(\csc(x)=7\) we draw a triangle

Answer 4

that ugly picture is a triangle where the hypotenuse is 7, the opposite side is 1, so the cosecant is 7
we need the third side, which by pythagoras is \(\sqrt{7^2-1^2}=\sqrt{48}\)

Answer 5

so would that equal Square root -48 for the final answer since its in the second quadrant?

Answer 6

now we need the cotangent, which is "adjacent over opposite" in other words
\[\frac{\sqrt{48}}{1}=\sqrt{48}\] but since you are in quadrant 2 it is negative, so your "final answer" is
\[-\sqrt{48}\] yes, what you said

Answer 7

ok thank you so much this was very helpful

Answer 8

yw