Identity:
sin θ / cos θ = tan θ
In the triangle from theta, the adjacent side is denoted as x, the opposite side is denoted as y and the hypotenuse is h.
So, we can create the identities for the trig functions using the specifics denotations.
sin θ = y/h
cos θ = x/h
tan θ = y/x
Now we can set up the equation to be:
y/h ÷ x/h = y/x
When we divide, we take the reciprocal of the 2nd term and multiply it with the 1st term.
y/h × h/x = y/x
It becomes:
yh/hx = y/x
We can cancel out the h since it is present in both the numerator and denominator.
Leaving us with:
y/x = y/x
Proving the tan θ identity.
