Pregunta
Convert the point \( (r, \theta, z)=\left(6, \frac{\pi}{2}, 4\right) \) to Cartesian coordinates. Give answers either as expressions, or decimals to at least one decimal place.
Ask by Simmons Conner. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The Cartesian coordinates are (0, 6, 4).
Solución
To convert the cylindrical coordinates \((r, \theta, z) = \left(6, \frac{\pi}{2}, 4\right)\) to Cartesian coordinates \((x, y, z)\), use the following formulas:
\[
\begin{align*}
x &= r \cos \theta \\
y &= r \sin \theta \\
z &= z
\end{align*}
\]
Substituting the given values:
\[
\begin{align*}
x &= 6 \cos\left(\frac{\pi}{2}\right) = 6 \times 0 = 0 \\
y &= 6 \sin\left(\frac{\pi}{2}\right) = 6 \times 1 = 6 \\
z &= 4
\end{align*}
\]
Therefore, the Cartesian coordinates are:
\[
(x, y, z) = (0, 6, 4)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
To convert the point \((r, \theta, z) = \left(6, \frac{\pi}{2}, 4\right)\) to Cartesian coordinates \((x, y, z)\), we can use the following relationships: 1. \(x = r \cdot \cos(\theta)\) 2. \(y = r \cdot \sin(\theta)\) 3. \(z = z\) Plugging in the given values: - \(r = 6\) - \(\theta = \frac{\pi}{2}\) - \(z = 4\) Calculating \(x\) and \(y\): \[ x = 6 \cdot \cos\left(\frac{\pi}{2}\right) = 6 \cdot 0 = 0 \] \[ y = 6 \cdot \sin\left(\frac{\pi}{2}\right) = 6 \cdot 1 = 6 \] So, the Cartesian coordinates are: \[ (x, y, z) = (0, 6, 4) \] Therefore, the point in Cartesian coordinates is \((0, 6, 4)\).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
