trig need help, with one last equation in my problem

Question

If , x in quadrant I, then find (without finding x)

sin(2x)= 2(4/9)(sqrt(65)/9)

cos(2x)= 1-2(4/9)^2

tan(2x) = ?

Answer 1

Chlo, it’s always easier for the tutors to work your problem if it is accurately written. When you wrote “sin(x) = 49”, it is confusing, because the value of sin is never more than 1. The value 49 is clearly a mistake. From the other lines of the problem, we can guess that it was actually supposed to be

“4 / 9”

Answer 2

sin/cos=tan so; 2(4/9)(sqrt(65)/9)/1-2(4/9)^2

8/9*(8.062...../9)/(1-2(16/81))

.888*.895 / 1-32/81

796.27 / .605

1.3162.....

atan=52.775.......°

Answer 3

Hi Chlo. Assuming your answers for sin(2x) and cos(2x) are correct (which I think they are), then by definition tan(2x) = sin(2x)/cos(2x). Remember to rationalize the denominator if necessary.

Robert