Step by step
The question
Question: write the polar point (5, 20°) 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 20° from the right side of the x-axis, going up and round.
Then go out 5.
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: 5 times cos 20°.
Careful!
x goes with cos, y goes with sin.
Swapped, we would get the point mirrored.
The calculator gives cos 20°: about 0.9397.
5 times 0.9397 is about 4.698.
To the nearest tenth, x ≈ 4.7.
Now y: 5 times sin 20°.
The calculator gives sin 20°: about 0.342.
5 times 0.342 is about 1.71.
To the nearest tenth, y ≈ 1.7.
So the point is (4.7, 1.7).
3 Check
Let's check on the grid.
From the point, go straight to the x-axis
and straight to the y-axis.
The grid shows x about 4.7 and y about 1.7.
The same.
Right!
Let's look back.
First: plot the point.
Then: use x = r cos θ, y = r sin θ.
Last: check.