Determinante de $$$\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right]$$$
Calculadora relacionada: Calculadora de Matriz de Cofatores
Sua entrada
Calcule $$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right|$$$.
Solução
O determinante de uma matriz 2x2 é $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right| = \left(\frac{\sqrt{3}}{2}\right)\cdot \left(- \sin{\left(t \right)}\right) - \left(\frac{\cos{\left(t \right)}}{2}\right)\cdot \left(0\right) = - \frac{\sqrt{3} \sin{\left(t \right)}}{2}$$$
Responder
$$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right| = - \frac{\sqrt{3} \sin{\left(t \right)}}{2}\approx - 0.866025403784439 \sin{\left(t \right)}$$$A