Question

If cos theta = -2/3, which of the following are possible? (More than one can be chosen) (will give medal & fan)

(listing answers in comments)

Answer 1

A. sin theta = sqrt(5)/3 and tan theta = sqrt(5)/2
B. sin theta = - sqrt(5)/3 and tan theta = 2/sqrt(5)
C. csc theta = -3/2 and tan theta = sqrt(5)/2
D. csc theta = 3/sqrt(5) and tan theta = - sqrt(5)/2

Answer 2

since \(\sin^2(x)+\cos^2(x)=1\) solve
\[b^2+\left(\frac{2}{3}\right)^2=1\] for \(b\)

Answer 3

or you could go right to
\[\sin(x)=\pm\sqrt{1-\left(\frac{2}{3}\right)^2}\]

Answer 4

I don't know what any of this means. My teacher failed to teach me any of this, so....

Answer 5

I usually don't ask for a straight up answer, but I'm seriously fed up with all of this.

Answer 6

ok
i will provide an answer

Answer 7

sine and cosine are points on the unit circle, whose equation is \(a^2+b^2=1\)
you have one of them at \(-\frac{2}{3}\) so we can solve
\[\left(-\frac{2}{3}\right)^2+b^2=1\] by squaring to get
\[\frac{4}{9}+b^2=1\\
b^2=1-\frac{4}{9}\\
b^2=\frac{5}{9}\\
b=\pm\sqrt{\frac{5}{9}}\\
b=\pm\frac{\sqrt5}{3}\]

Answer 8

all the steps are there, it is not terribly complicated, hope it is more clear

Answer 9

thank you