If x is an acute angle such that tan2x = -24/7, find sinx and cosx.
help? thanks
draw a right-triangle with acute angle 2x and opposite side 24 and adjacent side 7. use Pythagoras' theorem to find the hypotenuse.
then you will know that cos(2x) = (adjacent)/(hypotenuse)
then use the fact that $\displaystyle \cos 2x = 2 \cos^2 x - 1 = 1 - 2 \sin^2 x$ to find sin(x) and cos(x)
or you could solve.
tan(2x) = -24/7
=> sin(2x)/cos(2x) = -24/7
=> 7 sin(2x) = -24 cos(2x)
and use the double angle formulas to change everything to sine and cosine and continue