Question

describe the relationship between tan theta and cot 90- theta. is it similar to the relationship between cot theta and tan 90- theta? explain why this relationship works by using trig ratios and 30-60-90 triangles.

Answer 1

here is a triangle



then

\[\tan(\theta) = \frac{opp}{adj}\]

and

\[\cot(90 - \theta) = \frac{1}{\tan(90 - \theta)} = \frac{1}{\frac{adj}{opp}} = \frac{opp}{adj}\]

so

\[\tan(\theta) = \cot(90 - \theta)\]