I have a very basic trig question.
I have a right angle triangle. The triangle $y$-axis has size $0.1$ meters and the $x$-axis has $0.05$ meters. Now using the definition of tangent, I have $\tan \theta = \frac{opposite}{adjecent}$ therefore the angle for the triangle is $63.43$. Now, $\sin \theta =\sin(63.43) =0.56 $. Using the definition of $\sin$ I have that $\sin\theta=\frac{opposite}{hypotenuse}= \frac{.1}{\sqrt{(.1)^2+(.05)^2}} = 0.89$ which doesn't equal $\sin(63.43)$.
Not sure what I am doing wrong?
You forgot to use $\arcsin0.89$. Let's be sure of terms:
adjacent=$x=0.5\quad$opposite=$y=1\quad$ hypotenuse=$\sqrt{0.5^2+1^2}=1.118033989$.
$\tan\theta=\frac{opposite}{adjacent}=\frac{1}{0.5}=2\\ \implies \arctan 2=1.107148718^{radians}=63.43^\circ$.
$\sin\theta=\frac{1}{1.118033989}=0.8944\\ \implies\theta=\arcsin0.8944=1.107148718^{radians}=63.43^\circ$
$\cos\theta=\frac{0.5}{1.118033989}=0.4472\\ \implies\theta=\arccos0.4472=1.107148718^{ radians}=63.43^\circ $