convert the point to rectangular coordinates (5,5pi/6)
To convert a point from polar coordinates to rectangular coordinates, you can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
In this case, the given point is (5, 5π/6).
Step 1: Determine the value of r
The value of r represents the distance from the origin (0,0) to the point. In this case, r is given as 5.
Step 2: Determine the value of theta
The value of theta represents the angle from the positive x-axis to the line connecting the origin to the point. In this case, theta is given as 5π/6.
Step 3: Apply the formulas to find the rectangular coordinates
Using the formulas x = r * cos(theta) and y = r * sin(theta), substitute in the given values:
x = 5 * cos(5π/6)
y = 5 * sin(5π/6)
To compute cos(5π/6) and sin(5π/6), we can use the unit circle. The reference angle for 5π/6 is π/6, which corresponds to the point (√3/2, 1/2) on the unit circle.
x = 5 * (√3/2) = 5√3/2
y = 5 * (1/2) = 5/2
Therefore, the rectangular coordinates for the point (5, 5π/6) are (5√3/2, 5/2).