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Across: the Cosine

Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 2 of 55.

The sine is the point's height. The cosine is the other coordinate, the across: how far the point is right or left of the centre. cos⁡(θ)\cos\left(\theta\right) is the adjacent side divided by the radius 1, so it is the point's x coordinate. Left of the y-axis, it is negative.

A point P in the upper left of the circle: its across is negative and its height positive

So the point at θ is (cos⁡(θ)\cos\left(\theta\right), sin⁡(θ)\sin\left(\theta\right)). At 90° the point is straight up at (0, 1), so cos⁡(90∘)=0\cos\left(90^{\circ}\right) = 0. In a triangle a cosine is never negative. On the circle it can be.

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Challenge

The point has turned through 180°. Set its coordinates, cos(180°) and sin(180°). Pick a sign and a size for each.

Then press Check.

Start the lesson to read it in the interactive player and track your progress.

All lessons in Angles and the Unit Circle