Equações trigonométricas 2
Trigonometria: Infinito 11 A - Parte 1 Pág. 98 Ex. 64
Enunciado
Em cada um dos casos, encontre o valor de $\theta $, que verifica:
- $\begin{matrix}
\cos \theta =-0,5 & \wedge & \theta \in \left[ \pi ,2\pi \right] \\
\end{matrix}$ - $\begin{matrix}
sen\,\theta =-\frac{\sqrt{3}}{2} & \wedge & \theta \in \left[ \pi ,\frac{3\pi }{2} \right] \\
\end{matrix}$ - $\begin{matrix}
sen\,\theta =\frac{\sqrt{2}}{2} & \wedge & \theta \in \left[ \frac{\pi }{2},\pi \right] \\
\end{matrix}$ - $\begin{matrix}
sen\,\theta =-0,9 & \wedge & \theta \in \left[ \frac{3\pi }{2},\frac{5\pi }{2} \right] \\
\end{matrix}$ - $\begin{matrix}
tg\,\theta =-28,6362 & \wedge & -180{}^\text{o}<\theta <0{}^\text{o} \\
\end{matrix}$ - $\begin{matrix}
\cos\theta =-0,45399 & \wedge & -270{}^\text{o}<\theta <-180{}^\text{o} \\
\end{matrix}$ - $\begin{matrix}
\cos \theta =-\frac{\sqrt{2}}{2} & \wedge & \theta \in \left[ \pi ,2\pi \right] \\
\end{matrix}$ - $\begin{matrix}
tg\,\theta =-1,7 & \wedge & \theta \in \left] -\frac{\pi }{2},0 \right] \\
\end{matrix}$ - $\begin{matrix}
\cos \theta =-0,1 & \wedge & \theta \in \left] \pi ,2\pi \right[ \\
\end{matrix}$ - $\begin{matrix}
tg\,\theta =-1435 & \wedge & \theta \in \left[ \frac{\pi }{2},\pi \right[ \\
\end{matrix}$ - $\begin{matrix}
sen\,\theta =0,0174 & \wedge & 450{}^\text{o}<\theta <540{}^\text{o} \\
\end{matrix}$ - $\begin{matrix}
sen\,\theta =-0,5150 & \wedge & 180{}^\text{o}<\theta <270{}^\text{o} \\
\end{matrix}$
Resolução
-
$\begin{matrix}
\begin{matrix}
\cos \theta =-0,5 & \wedge & \theta \in \left[ \pi ,2\pi \right] \\
\end{matrix} & \Leftrightarrow & \theta = \\
\end{matrix}\frac{4\pi }{3}$
- $\begin{matrix}
\begin{matrix}
sen\,\theta =-\frac{\sqrt{3}}{2} & \wedge & \theta \in \left[ \pi ,\frac{3\pi }{2} \right] \\
\end{matrix} & \Leftrightarrow & \theta = \\
\end{matrix}\frac{4\pi }{3}$
- $\begin{matrix}
\begin{matrix}
sen\,\theta =\frac{\sqrt{2}}{2} & \wedge & \theta \in \left[ \frac{\pi }{2},\pi \right] \\
\end{matrix} & \Leftrightarrow & \theta = \\
\end{matrix}\frac{3\pi }{4}$
- $\begin{matrix}
\begin{matrix}
sen\,\theta =-0,9 & \wedge & \theta \in \left[ \frac{3\pi }{2},\frac{5\pi }{2} \right] \\
\end{matrix} & \Leftrightarrow & \theta \simeq 5,2 \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
tg\,\theta =-28,6362 & \wedge & -180{}^\text{o}<\theta <0{}^\text{o} \\
\end{matrix} & \Leftrightarrow & \theta \simeq -88{}^\text{o} \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
\cos\theta =-0,45399 & \wedge & -270{}^\text{o}<\theta <-180{}^\text{o} \\
\end{matrix} & \Leftrightarrow & \theta \simeq -243{}^\text{o} \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
\cos \theta =-\frac{\sqrt{2}}{2} & \wedge & \theta \in \left[ \pi ,2\pi \right] \\
\end{matrix} & \Leftrightarrow & \theta = \\
\end{matrix}\frac{5\pi }{4}$
- $\begin{matrix}
\begin{matrix}
tg\,\theta =-1,7 & \wedge & \theta \in \left] -\frac{\pi }{2},0 \right] \\
\end{matrix} & \Leftrightarrow & \theta \simeq -1,04 \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
\cos \theta =-0,1 & \wedge & \theta \in \left] \pi ,2\pi \right[ \\
\end{matrix} & \Leftrightarrow & \theta \simeq 4,6 \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
tg\,\theta =-1435 & \wedge & \theta \in \left[ \frac{\pi }{2},\pi \right[ \\
\end{matrix} & \Leftrightarrow & \theta \simeq 1,6 \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
sen\,\theta =0,0174 & \wedge & 450{}^\text{o}<\theta <540{}^\text{o} \\
\end{matrix} & \Leftrightarrow & \theta \simeq 539{}^\text{o} \\
\end{matrix}$
- $\begin{matrix}
\begin{matrix}
sen\,\theta =-0,5150 & \wedge & 180{}^\text{o}<\theta <270{}^\text{o} \\
\end{matrix} & \Leftrightarrow & \theta \simeq 211{}^\text{o} \\
\end{matrix}$
