convert 5, pi/4 to rectangular coordinates
To convert a point from polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In the given question, the polar coordinates are 5 and π/4.
To convert 5, π/4 to rectangular coordinates, you need to substitute these values into the formulas.
x = 5 * cos(π/4)
y = 5 * sin(π/4)
To evaluate the trigonometric functions, we need to use the decimal value of π, which is approximately 3.14159.
x = 5 * cos(0.78539)
y = 5 * sin(0.78539)
Using a calculator or a programming language that supports trigonometric functions, you can calculate the values of cos(0.78539) and sin(0.78539).
x = 5 * 0.70710 ≈ 3.53553
y = 5 * 0.70710 ≈ 3.53553
Therefore, the rectangular coordinates for 5, π/4 are approximately (3.53553, 3.53553).