convert the point with polar coordinates (2,7pi/6) into rectangular coordinates.
To convert a point with polar coordinates (r, θ) into rectangular coordinates (x, y), you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, the polar coordinates given are (2, 7π/6).
First, let's calculate x:
x = 2 * cos(7π/6)
To find cos(7π/6), we need to convert the angle to radians. Since π radians is equivalent to 180 degrees, we can multiply 7π/6 by (180/π) to convert it into degrees.
Angle in degrees = (7π/6) * (180/π) = (7 * 180) / 6 = 210 degrees
Now, we can find cos(7π/6) using a unit circle or a trigonometric table. The value of cos(210 degrees) is -0.866.
Therefore, x = 2 * (-0.866) = -1.732
Next, let's calculate y:
y = 2 * sin(7π/6)
Similar to before, we need to convert the angle into degrees:
Angle in degrees = (7π/6) * (180/π) = (7 * 180) / 6 = 210 degrees
Now, sin(210 degrees) = -0.5
Therefore, y = 2 * (-0.5) = -1
Hence, the rectangular coordinates corresponding to the polar coordinates (2, 7π/6) are approximately (-1.732, -1).