2. The polar coordinates of a point are given. Find the rectangular coordinates of each point.
a. (5,(π / 4))
b. (-2,(π / 6))
NOTE: I tried to do these myself and got that:
a= (4.99,0.27)
b=(-1.99,-0.11)
Which I know these are wrong, so I don't know how to do them..
For any (r,Ø)
x = rcosØ, y = rsinØ
so
x = 5cos(π/4) , y = 5sin(π/4)
x = 5√2/2 , y = 5√2/2
so you have the point (5√2/2 , 5√2/2)
(I don't see why you would want to write that in decimals, since you have to round it)
appr (3.5355 , 3.5355)
do the 2nd question in the same way
To find the rectangular coordinates (x, y) from the given polar coordinates (r, θ), you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
Now, let's solve the given problems:
a. (5, (π/4))
To find the rectangular coordinates, we need to plug in the values of r and θ into the formulas.
x = 5 * cos(π/4)
y = 5 * sin(π/4)
Using a calculator, evaluate the cos(π/4) and sin(π/4) to get the decimal values:
x = 5 * 0.7071 ≈ 3.5355
y = 5 * 0.7071 ≈ 3.5355
So the rectangular coordinates of the point (5, (π/4)) are approximately (3.5355, 3.5355).
b. (-2, (π/6))
Again, apply the formulas:
x = -2 * cos(π/6)
y = -2 * sin(π/6)
Evaluate the cos(π/6) and sin(π/6) using a calculator:
x = -2 * 0.866 ≈ -1.732
y = -2 * 0.5 = -1.000
Therefore, the rectangular coordinates of the point (-2, (π/6)) are approximately (-1.732, -1.000).
Your previous answers, a = (4.99, 0.27) and b = (-1.99, -0.11), are incorrect because they do not reflect the application of the formulas mentioned above.