# Math Help - exact value of trig function

1. ## exact value of trig function

What is the exact value of

sin²36°

2. $\sin36^\circ=\sin(2\cdot18^\circ)=2\sin18^\circ\co s18^\circ.$

$\sin36^\circ=\cos54^\circ\implies2\sin18^\circ\cos 18^\circ=\cos(3\cdot18^\circ),$ so $\cos(3\cdot18^\circ)=4\cos^318^\circ-3\cos18^\circ.$

Now, $2\sin18^\circ=4\cos^218^\circ-3.$

From here you can get $\sin18^\circ$ & $\cos18^\circ,$ then plug'em into the initial formula and you're done.