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Relationships between sine, cosine and tangent

Relationships between sine, cosine and tangent

IP 2
7 marks

In triangle \(ABC\), \(\angle C=90^\circ\), \(\angle A=\theta\), \(BC=a\), \(AC=b\) and \(AB=c\).

  1. Show that \(\tan\theta=\dfrac{\sin\theta}{\cos\theta}\) and \(\sin^2\theta+\cos^2\theta=1\).[3]
  2. Given that \(\sin\theta=\dfrac{5}{13}\), find the exact values of \(\cos\theta\) and \(\tan\theta\).[2]
  3. Explain why \(0<\sin\theta<1\) for every acute angle \(\theta\).[2]

Solution:

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Answer:(a) Shown (b) \(\cos\theta=\dfrac{12}{13}\), \(\tan\theta=\dfrac{5}{12}\) (c) \(\sin\theta=\dfrac{a}{c}\) with \(0<a<c\)

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