Question

if cos(t)=0.8 and t is in 3rd quad, find sin(2t)
is this 0.96 for the answer?

Answer 1

2sin(x)cos(x) = sin(2x)

so

2sin(x)(0.8) = sin(2x)
so you need to find cos(x)

so we use the definition
cos^(2)(x) + sin^(2)(x) = 1

sub 0.8 into the formula
and you should get something like this:

\[\cos(x) = \pm \sqrt{1-(0.8)^2}\]

Now to remember what is positive and what is negative in the quadrants remember, All Students Take calculus".
Because
QI = (A)ll positive,
QII = (S)ine, csc is positive
QIII = (T)an cot is positive
QIV = Cos and sec are positive

so sin would be negative.

Follow these steps and you should be fine