Question

Dado $sen a = cos a - 0,2$ calcule sen2a !
Por favor ajudem!

Answer 1

Da identidade trigonométrica,

\sin(2x) = 2 \sin(x) \cos(x)sin(2x)=2sin(x)cos(x)

Logo,

\begin{gathered} \sin(2a) = 2 \sin(a) \cos(a) \\ = 2( \cos(a) - 0.2) \cos(a) \\ =( 2 \cos(a) - 0.4) \cos(a) \\ = 2 { \cos(a) }^{2} - 0.4 \cos(a) \\ \\ ou \\ \\ \sin(2a) = 2 {( \sin(a) + 0.2) }^{2} - 4( \sin(a) + 0.2) \\ = 2( { \sin(a) }^{2} + 2 \sin(a) \times 0.2 + {0.2}^{2} ) - 4 \sin(a) - 0.8 \\ = 2 { \sin(a) }^{2} + 0.8 \sin(a) + 0.08 - 4 \sin(a) - 0.8 \\ = 2 { \sin(a) }^{2} - 3.2 \sin(a) - 0.72\end{gathered}sin(2a)=2sin(a)cos(a)=2(cos(a)−0.2)cos(a)=(2cos(a)−0.4)cos(a)=2cos(a)2−0.4cos(a)ousin(2a)=2(sin(a)+0.2)2−4(sin(a)+0.2)=2(sin(a)2+2sin(a)×0.2+0.22)−4sin(a)−0.8=2sin(a)2+0.8sin(a)+0.08−4sin(a)−0.8=2sin(a)2−3.2sin(a)−0.72