Question

find cos theta if sin theta =-2/3 and falls in quadrant 3 HELP ASAP PLEASE

Answer 1

Why asap ... are you taking a quiz or something?

Answer 2

Do you know what SOHCAHTOA is?

Answer 3

SOHCAHTOA allows us to know which two sides must be divided in order to find the sine, cosine or tangent. So for example, SOH means that \[Sin \theta = \frac{ O }{ H }\].

Answer 4

Since you've been told that \[Sin \theta = \frac{ -2 }{ 3 }\] then we can deduce that O = -2 and H = 3

Answer 5

By using pythagoras theorem we can deduce that A =

\[h ^{2} = a^{2} + o^{2} \] 9 = 4 + a^2
a= sqrt{5}

Answer 6

however since we are of the third quadrant, A and O are always negative therefore a =
\[-\sqrt{5}\]

Answer 7

Now we look at SOHCAHTOA again to find out that \[\cos \theta = \frac{ A }{ H }\] Which gives us \[\cos \theta = \frac{ -\sqrt{5} }{ 3 }\]

Answer 8

And we are done.