Question

The tangent of an angle is equal to the ratio of its sine divided by its cosine: true or false?

Answer 1

The tangent of an angle is equal to the ratio of its sine divided by its cosine: true or false? Please give detailed answer

By definition:

$$t g \alpha \stackrel {\text {a d}} {\approx} \frac {A B}{O A}$$ $$\sin \alpha \stackrel {\text {a d}} {\approx} \frac {A B}{O B}$$ $$\cos \alpha \stackrel {\text {a d}} {\approx} \frac {O A}{O B}$$ $$\frac {\sin \alpha}{\cos \alpha} = \frac {A B}{O B}; \frac {O A}{O B} = \frac {A B}{O B} \frac {O B}{O A} = \frac {A B}{O A} = t g \alpha$$

Answer: True