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10
2+2×4.
Class 12 · English Medium · Cambridge · Mathematics
Geometry, measurement and trigonometry readiness
Use vector lines and trigonometric identities with a defined domain.
About this lesson and its coverage
Original Kidemy Class 12 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
A vector line can be written r=a+tb, where a is a point and b a direction. An intersection must satisfy all coordinate equations with consistent parameters. Trigonometric identities hold on domains where their expressions are defined.
Worked example
Line r=(1,2)+t(3,−1) passes through(7,0) at t=2. Since sin²θ+cos²θ=1, a known sine can give cosine’s magnitude, but its sign needs a quadrant.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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1
4+0−3.
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0.8
Positive√(1−0.36).
Write in your own words. A guardian or teacher should review this response.
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Angles in different quadrants can share a sine while cosines have opposite signs.
Use quadrant information.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
x gives t=4 and y gives t=4, so it lies on the line.
Use one consistent parameter.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Solve a vector-line membership problem and explain a trigonometric sign choice.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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