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円 · Unit circle and trigonometry
Scroll of the Circle
Walk around a circle with radius 1. Your height is sine, your sideways distance is cosine.
Height and Width
On the unit circle, sin is the y-coordinate and cos is the x-coordinate. At the top of the circle you are at height 1.
sin 90°
- → 90° is straight up
- → Height there is 1
Answer: 1
cos 0° = 1 · sin 0° = 0 · cos 90° = 0 · sin 180° = 0 · cos 180° = −1
Practice: Try sin 270° and cos 180°.
Half-Circle Rule
Half a circle is 180° and also π radians. Every angle is a fraction of that.
45° = ? rad
- → 45 is 180 ÷ 4
- → So π ÷ 4
Answer: π/4
90° = π/2 · 60° = π/3 · 30° = π/6 · 360° = 2π
Practice: Try 120° and sin(π/2).
Into the dojo
Practise with the Circle ◯ technique from blue belt.
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