幾何学と三角関数
導入済み| English | 意味 |
|---|---|
| similarity/ˌsɪmɪˈlærɪti/ | 類似性 |
| radian/ˈreɪdɪən/ | ラジアン |
A decision before an answer
- A map doubles every length. The represented area grows by four, not two.
- Your goal: Use area, volume and similarity.
Read the relationship
- Similarity preserves corresponding angles and length ratios. Areas scale by k² and volumes by k³.
- Apply right-triangle ratios and the Pythagorean theorem.
A circle has equation (x−2)²+(y+3)²=25. Centre?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Compare the signs with (x−h)²+(y−k)².
Use the defining rule
- For a right triangle, sin is opposite/hypotenuse, cos adjacent/hypotenuse, and tan opposite/adjacent.
- Use circle equations, arcs and angle relationships.
A cube’s edge doubles. Its volume grows by:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Three independent lengths each double: 2³=8.
Check the conditions
- A circle with centre (h,k) and radius r has (x−h)²+(y−k)²=r².
- Use circle equations, arcs and angle relationships.
A right triangle has legs 6 and 8. c²=6²+8²=100, so c=10. For the angle opposite 6, sin θ=6/10=0.6. A similar triangle enlarged by factor 3 has area nine times the original.
For radius 3 and angle 2 radians, arc length is ____.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
s=rθ=3×2=6 in the radius unit.
Apply the task format
- A full turn is 360° or 2π radians. Arc length is rθ only when θ is in radians.
- Use circle equations, arcs and angle relationships.
Radius and diameter differ by a factor of two. Using diameter in πr² makes the area four times too large.
このケースに当てはまる答えはどれか？
面積、体積、相似を用いる
sin θ can exceed 1 in a real right triangle.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The opposite side cannot exceed the hypotenuse.
Keep the distinctions
- similarity 相似 — Equal angles and proportional corresponding lengths.
- radian 弧度 — Angle measure defined by arc length divided by radius.
- Use area, volume and similarity.
- Apply right-triangle ratios and the Pythagorean theorem.
- Use circle equations, arcs and angle relationships.
Match each term with its precise meaning in this lesson.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
The order follows the stated process; check each stage before the next.