Why trigonometric ratios stay constant
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Log in to continueUse similar right triangles to explain why sine, cosine and tangent depend on the angle, not the triangle size.
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A right triangle has opposite leg 3, adjacent leg 4 and hypotenuse 5 relative to angle θ. Find sine θ.
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Answer: 3/5
- The sine ratio uses 3/5.
- Divide numerator and denominator by 1.
- The ratio is 3/5.
- 3 ÷ 5 = 3/5.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Use similar right triangles to explain why sine, cosine and tangent depend on the angle, not the triangle size.
Read the official VCAA curriculum description (VC2M9SP01)
These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.
Activities to practise beyond the quiz
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M9SP01-C01Identify opposite, adjacent and hypotenuse.
- VC2M9SP01-C02Show why a length ratio is unchanged by enlargement.
- VC2M9SP01-C03Use similarity constructions or digital tools to justify constant ratios.
- VC2M9SP01-C04Apply and explain why trigonometric ratios stay constant using calculate and explain each step.
- VC2M9SP01-C05Apply and explain why trigonometric ratios stay constant using work backwards from what is known.
- VC2M9SP01-C06Apply and explain why trigonometric ratios stay constant using read and connect representations.
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Descriptor-derived subskills
- D01Name the correct ratioIdentify opposite, adjacent and hypotenuse.
- D02Cancel the common scaleShow why a length ratio is unchanged by enlargement.
- D03Calculate and explain each stepApply and explain why trigonometric ratios stay constant using calculate and explain each step.
- D04Work backwards from what is knownApply and explain why trigonometric ratios stay constant using work backwards from what is known.
- D05Read and connect representationsApply and explain why trigonometric ratios stay constant using read and connect representations.