Why does my child think cos 120° = 1/2?
Your child gets the sign or the quarter of the circle wrong, such as cos 120° as 1/2 instead of −1/2.
Why children do it
The size, 1/2, comes from the same triangle as cos 60°, so it feels right. But on the unit circle 120° is to the left of the y-axis, where x-coordinates, the cosines, are negative: cos 120° = −1/2. A quick sketch of the circle shows the sign.
How to help at home
Ask them to sketch the angle on a circle: left of the middle, cos is negative; below it, sin is.
The right way
On the unit circle, the point at 120° is (cos 120°, sin 120°). What is its x−coordinate, exactly?
- −1/2The same size as cos 60°, but 120° is left of the y-axis, so negative.
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