I'm trying to find all the solutions to
$$ \sin(5a) = \cos(7a) $$
My attempt is to use the identity $\sin a = \cos \frac{\pi}{2} -a$.
Setting $7a = \frac{\pi}{2} - 5a$, gives me $a = \frac{\pi}{24}$ and one solution is:
$$ \sin(5 \cdot \frac{\pi}{24} ) = cos(\frac{\pi}{2} - 5 \cdot \frac{\pi}{24}) $$
If I plug this into geogebra I get:
But if I put this into a calculater I get $\sin(5 \cdot \frac{\pi}{24} ) \approx 0.608 \text{ and } cos(\frac{\pi}{2} - 5 \cdot \frac{\pi}{24}) \approx 0.1305$. I'm not very familliar with trig in general, but I was expecting them to be equal. What am I missing?