Question

If, P(x,y) is a point on the unit circle determined by real number δ, then tanδ = what

Answer 1

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse} =\cfrac{y}{r} =\cfrac{1}{csc(\theta)} \\ \quad \\\\ % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} =\cfrac{x}{r} =\cfrac{1}{sec(\theta)} \\ \quad \\\\ % tangent tan(\theta)=\cfrac{opposite}{adjacent} =\cfrac{y}{x} =\cfrac{sin(\theta)}{cos(\theta)}$

$\bf cot(\theta)=\cfrac{adjacent}{opposite} =\cfrac{x}{y} =\cfrac{cos(\theta)}{sin(\theta)} \\ \quad \\\\ % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} =\cfrac{r}{y} =\cfrac{1}{sin(\theta)} \\ \quad \\\\ % secant sec(\theta)=\cfrac{hypotenuse}{adjacent} =\cfrac{r}{x} =\cfrac{1}{cos(\theta)}\\\\ -------------------------------\\\\ P(x,y)\implies \delta\qquad tan(\delta)=\cfrac{y}{x}$