Question

Seja $\alpha$ um ângulo agudo tal que cos $\alpha = \frac{15}{17}$ , determine sen $\alpha$.

Answer 1

Sena² + Cosa²=1
Sena²+(15/17)²=1
Sena²=1-225/289
Sena²=64/289
Sena=8/17

Answer 2

Utilizando a seguinte identidade trigonométrica:
$(sen\alpha)^2+(cos\alpha)^2=1\\\\ Sabemos\ o\ valor\ do\ cosseno:\\\\ (sen\alpha)^2+(\frac{15}{17})^2=1\\\\ (sen\alpha)^2=1-(\frac{15}{17})^2\\\\ (sen\alpha)^2=1-\frac{15^2}{17^2}\\\\ (sen\alpha)^2=1-\frac{225}{289}\\\\ (sen\alpha)^2=\frac{289}{289}-\frac{225}{289}\\\\ (sen\alpha)^2=\frac{289-225}{289}\\\\ (sen\alpha)^2=\frac{64}{289}\\\\ sen \alpha=\sqrt{\frac{64}{289}}\\\\ sen \alpha=\frac{\sqrt{64}}{\sqrt{289}}\\\\ \boxed{sen \alpha=\frac{8}{17}}$

Bons estudos!