Step by step
The question
Question: write the polar point (6, 90°) in rectangular form (x, y).
1 Plot the point
Draw the polar grid: circles 1, 2, 3 around the center, and lines for the angles.
Turn 90° from the right side of the x-axis, going up and round.
Then go out 6.
2 Use x = r cos θ, y = r sin θ
For any polar point: x = r cos θ and y = r sin θ.
They come from the right triangle under the point.
First x: 6 times cos 90°.
Careful!
x goes with cos, y goes with sin.
Swapped, we would get the point mirrored.
cos 90° is 0.
We know it from the special triangles.
Put it in.
6 times 0 is 0.
Now y: 6 times sin 90°.
sin 90° is 1.
We know it from the special triangles.
Put it in.
6 times 1 is 6.
So the point is (0, 6).
3 Check
Let's check on the grid.
From the point, go straight to the x-axis
The grid shows x 0 and y 6.
The same.
Right!
Let's look back.
First: plot the point.
Then: use x = r cos θ, y = r sin θ.
Last: check.