Answer:
The polar coordinates are as follow:
a. (6,2π)
b. (18, π/3)
c. (2√2 , 3π/4)
d. (2, 5π /6)
Step-by-step explanation:
To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .
To calculate r, we use Pythagorean theorem:
r = ---- (1)
To calculate the θ, first we will find out the θ
' using the inverse of cosine as it is easy to calculate.
So, θ
' =
cos
⁻¹ (x/r)
If y ≥ 0 then θ = ∅
If y < 0 then θ = 2
π − ∅
For a. (6,0)
Sol:
Using the formula in equation (1). we get the value of r as:
r =
r = 6
And ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (6/6)
∅ =cos
⁻¹ (1) = 2π
As If y ≥ 0 then θ = ∅
So ∅ = 2π
The polar coordinates are (6,2π)
For a. (9,9/)
Sol:
r = 9 + 3(3) = 18
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (9/18)
∅ = cos
⁻¹ (1/2) = π/3
As If y ≥ 0 then θ = ∅
then θ = π/3
The polar coordinates are (18, π/3)
For (-2,2)
Sol:
r =√( (-2)²+(2)² )
r = 2 √2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (-2/ 2 √2)
∅ = 3π/4
As If y ≥ 0 then θ = ∅
then
θ = 3π/4
The polar coordinates are (2√2 , 3π/4)
For (-√3, 1)
Sol:
r = √ ((-√3)² + 1²)
r = 2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ ( -√3/2)
∅ = 5π /6
As If y ≥ 0 then θ = ∅
So θ = 5π /6
The polar coordinates are (2, 5π /6)
Hello from MrBillDoesMath!
Answer:
Suppose the ordered pair is (x.y). Substitute these values in the linear equality to see if it is true,
Example. Consider the point (7, -4). Is it a solution of the linear inequality
3x < 4y - 9? Let's check to find out.
Check:
Is 3 (7) < 4 (-4) - 9 true ?
Is 21 < -16 -9 = -25 ??
NO!
So (7,-4) is NOT a solution of the linear inequality.
Thank you,
MrB
35% because 35% of 80 is 28
Answer:
65
Step-by-step explanation:
it is the largest cup so it is 65
Answer:
75%
Step-by-step explanation:
44*75% = 33