Explanation

If you know:

• Magnitude r

• Direction θ

You can find components using trig:

x = r cos θ
y = r sin θ

Vector = ⟨r cos θ, r sin θ⟩

Example:
Magnitude = 10
Angle = 30°

⟨10cos30°, 10sin30°⟩ = ⟨5√3, 5⟩

Quiz

1. What formula gives the x-component?

2. What formula gives the y-component?

3. Which trig function uses cosine?

4. Which uses sine?

5. Does direction matter?

Answer Key

1. r cos θ

2. r sin θ

3. x-component

4. y-component

5. Yes