Question

VEAN LA FOTO, rápido xfavor​

Answer 1

Respuesta:

Explicación paso a paso:

Recordemos lo siguiente:

$\sin(\theta)=\frac{y}{r}\\\\\cos(\theta)=\frac{x}{r}\\\\\tan(\theta)=\frac{y}{x}\\\\\cot(\theta)=\frac{x}{y}\\\\\sec(\theta)=\frac{r}{x}\\\\\csc(\theta)=\frac{r}{y}\\\\r=\sqrt{x^{2}+y^{2}}$

Sustituyendo las coordenadas del punto en las expresiones anteriores nos queda:

$r=\sqrt{(-8)^{2}+(15)^{2}}=\sqrt{289}=17\\\\\sin(\alpha)=\frac{15}{17}\\\\\cos(\alpha)=\frac{x}{r}=\frac{-8}{17}=-\frac{8}{17}\\\\\tan(\alpha)=\frac{y}{x}=\frac{15}{-8}=-\frac{15}{8}\\\\\cot(\alpha)=\frac{x}{y}=\frac{-8}{15}=-\frac{8}{15}\\\\\sec(\alpha)=\frac{r}{x}=\frac{17}{-8}=-\frac{17}{8}\\\\\csc(\alpha)=\frac{r}{y}=\frac{17}{15}$

Saludos