The rectangular and polar coordinates of a
point are (x, y) and (r, θ), where x = 4 and
θ = 38◦
.
Determine the value of r.
since x = r cosθ
r = x/cosθ
To determine the value of r, we can use the formula:
r = √(x^2 + y^2)
However, we are given the values of x and θ in this case, not y. So, we need to find the value of y using the given information.
First, let's convert the angle θ from degrees to radians. To do this, we multiply θ by π/180:
θ = 38° * π/180 ≈ 0.6632 radians.
Since x is given as x = 4, and we know that x = r * cos(θ), we can rearrange the formula and solve for r:
r = x / cos(θ)
Let's substitute the values into the formula:
r = 4 / cos(0.6632) ≈ 4.418
Therefore, the value of r is approximately 4.418.