Question

No triângulo abaixo, determine:
a) a secante do ângulo do ângulo do vértice A
b) a cotangente do ângulo do vértice B.
c) o seno do ângulo do ângulo do vértice C

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf cos~\hat A=cos\,60^\circ=\dfrac{1}{2}\\\sf sec\,\hat A=sec\,60^\circ=2\\\tt b)~\sf cotg\,\hat B=cotg\,45^\circ=1\\\tt c)~\sf sen\,\hat C=sen\,75^\circ= sen(30^\circ+45^\circ)\\\sf sen(75^\circ)=sen\,30^\circ\cdot cos\,45^\circ+sen\,45^\circ\cdot cos\,30^\circ\\\sf sen\,75^\circ=\dfrac{1}{2}\cdot\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}} {2}\cdot\dfrac{\sqrt{3}}{2}\\\sf sen\,75^\circ=\dfrac{\sqrt{2}+\sqrt{6}}{4}\end{array}}$