Question

Me ajudem por favor Se cos ⁡x = −4 / 5, e$pi\ \textless \ x\ \textless \ 3pi2$, o que é sin⁡$(x+pi/2)$

Answer 1

Aplique a fórmula do seno da soma:

    $\mathsf{sen(\alpha+\beta)=sen\,\alpha\,cos\,\beta+cos\,\alpha\,sen\,\beta}$

Portanto,

    $\mathsf{sen\!\left(x+\dfrac{\pi}{2}\right)=sen\,x\cdot cos\,\dfrac{\pi}{2}+cos\,x\cdot sen\,\dfrac{\pi}{2}}\\\\\\ \mathsf{\Longleftrightarrow\quad sen\!\left(x+\dfrac{\pi}{2}\right)=sen\,x\cdot 0+cos\,x\cdot 1}\\\\\\ \mathsf{\Longleftrightarrow\quad sen\!\left(x+\dfrac{\pi}{2}\right)=0+cos\,x}\\\\\\ \mathsf{\Longleftrightarrow\quad sen\!\left(x+\dfrac{\pi}{2}\right)=cos\,x}$

para todo $\mathsf{x\in\mathbb{R}.}$

Em particular, se cos x = -4/5, então

    $\mathsf{\Longleftrightarrow\quad sen\!\left(x+\dfrac{\pi}{2}\right)=cos\,x=-\,\dfrac{4}{5}\quad\longleftarrow\quad resposta.}$

Dúvidas? Comente.

Bons estudos! :-)