Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Define sec theta, cosec theta and cot theta. • Use identities 1+tan^2 theta=sec^2 theta and 1+cot^2 theta=cosec^2 theta. • Know domains, ranges and graphs of arcsin x, arccos x and arctan x.
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Learning objective
• Use compound-angle identities and the double-angle identity for tan. • Derive double-angle identities from compound-angle identities.
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Learning objective
• Solve more complex trigonometric equations in finite intervals. • Use reciprocal, inverse and compound-angle identities where appropriate.
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Learning objective
• Use position vectors, displacement vectors and directed line segment representation. • Use base vectors i, j, k; components, magnitude, unit vectors and vector algebra. • Prove geometric properties using vectors.
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Learning objective
• Use scalar product, angle between vectors, perpendicular and parallel vector conditions. • Apply v dot w = |v||w| cos theta and scalar product properties.
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Learning objective
• Use vector, parametric and Cartesian equations of lines in 2D and 3D. • Find angles between lines using scalar product of direction vectors. • Interpret line parameter as time in simple kinematics.
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Learning objective
• Distinguish coincident, parallel, intersecting and skew lines. • Find points of intersection where they exist.
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Learning objective
• Use vector/cross product v x w = |v||w| sin theta n. • Know properties, right-hand rule direction and parallel-vector condition. • Use |v x w| for parallelogram and triangle areas.
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Learning objective
• Use vector equations of a plane r=a+lambda b+mu c and r dot n=a dot n. • Use Cartesian equation ax+by+cz=d.
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Learning objective
• Find intersections of line-plane, two-plane and three-plane systems. • Find angles between a line and a plane, and between two planes. • Interpret solutions geometrically.
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