Physics worksheet for finding x and y components of vectors using trigonometry.

Let’s solve each vector one by one. We’ll find the x and y components using trigonometry:
- x-component = magnitude × cos(angle)
- y-component = magnitude × sin(angle)

But we must be careful about the angle — it’s always measured from the positive x-axis (right side), going counterclockwise.

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First Vector: 12 m at 30°

This is in the first quadrant, so both x and y are positive.

→ x = 12 × cos(30°)
cos(30°) ≈ 0.866
x ≈ 12 × 0.866 = 10.392 m

→ y = 12 × sin(30°)
sin(30°) = 0.5
y = 12 × 0.5 = 6.0 m

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Second Vector: 25 m/s at 60°

Also in the first quadrant → both x and y positive.

→ x = 25 × cos(60°)
cos(60°) = 0.5
x = 25 × 0.5 = 12.5 m/s

→ y = 25 × sin(60°)
sin(60°) ≈ 0.866
y ≈ 25 × 0.866 = 21.65 m/s

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Third Vector: 15 m/s at 150°

Angle is 150° — that’s in the second quadrant (between 90° and 180°).
In second quadrant:
→ x-component is NEGATIVE (leftward)
→ y-component is POSITIVE (upward)

We can still use the same formulas, but let’s think carefully:

The reference angle (from the negative x-axis) is 180° - 150° = 30°.

So:
→ x = 15 × cos(150°)
cos(150°) = -cos(30°) ≈ -0.866
x ≈ 15 × (-0.866) = -12.99 m/s

→ y = 15 × sin(150°)
sin(150°) = sin(30°) = 0.5
y = 15 × 0.5 = 7.5 m/s

*(You can also think: “It’s like a 30° triangle pointing left and up.”)*

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✔ Let me double-check all calculations:

1. 12×cos(30)=12×√3/2≈12×0.866=10.392 ✔️
12×sin(30)=12×0.5=6 ✔️

2. 25×cos(60)=25×0.5=12.5 ✔️
25×sin(60)=25×√3/2≈25×0.866=21.65 ✔️

3. 15×cos(150)=15×(-√3/2)≈-12.99 ✔️
15×sin(150)=15×0.5=7.5 ✔️

All good!

Final Answer:

For 12 m at 30°:
x = 10.4 m
y = 6.0 m

For 25 m/s at 60°:
x = 12.5 m/s
y = 21.7 m/s

For 15 m/s at 150°:
x = -13.0 m/s
y = 7.5 m/s

*(Rounded to one decimal place for simplicity, as typical in high school physics.)*