Question

dado el sen\alpha =\frac{3}{5} hallar las demás razones trigonométricas

Answer 1

Respuesta:

cos $\alpha$ = $\frac{4}{5}$

tg $\alpha$ = $\frac{3}{4}$

cosec $\alpha$ = $\frac{5}{3}$

sec $\alpha$ = $\frac{5}{4}$

cotg $\alpha$ = $\frac{4}{3}$

Explicación paso a paso:

¿cos $\alpha$? ⇒ sen²$\alpha$ + cos²$\alpha$ = 1 ⇒ ($\frac{3}{5}$)² + cos²$\alpha$ = 1 ⇒ cos²$\alpha$ = 1 - $\frac{9}{25}$ ⇒ cos²$\alpha$ = $\frac{16}{25}$ ⇒

⇒ cos $\alpha$ = √$\frac{16}{25}$ ⇒ cos$\alpha$ = $\frac{4}{5}$

¿tg $\alpha$? ⇒ tg$\alpha$ = $\frac{sen\alpha }{cos\alpha }$ ⇒ tg$\alpha$ = $\frac{3}{5}$ ÷ $\frac{4}{5}$ ⇒ tg$\alpha$ = $\frac{3}{4}$

cosec$\alpha$ = $\frac{1}{sen\alpha }$ = 1 ÷ $\frac{3}{5}$ = $\frac{5}{3\\}$

sec$\alpha$ = $\frac{1}{cos\alpha }$ = 1 ÷ $\frac{4}{5}$ = $\frac{5}{4}$

cotg$\alpha$ = $\frac{1}{tg\alpha }$ = 1 ÷ $\frac{3}{4}$ = $\frac{4}{3}$