A handyman wants to check a calculator result without replacing its flat battery, to avoid an unplanned cost. Using the exact values of \(\sin 60^\circ\) an...
Question 1 Report
A handyman wants to check a calculator result without replacing its flat battery, to avoid an unplanned cost. Using the exact values of \(\sin 60^\circ\) and \(\cos 60^\circ\), show that \(\tan 60^\circ = \sqrt{3}\). (3)
Answer Details
Since \(\tan\theta=\frac{\sin\theta}{\cos\theta}\) for any angle, the exact value of \(\tan60^\circ\) can be built directly from the exact values of \(\sin60^\circ\) and \(\cos60^\circ\), which come from a half-equilateral triangle with sides \(1,\ 2\) and \(\sqrt3\).
\(\sin60^\circ=\frac{\sqrt3}{2}\) and \(\cos60^\circ=\frac12\) [1 mark]
\(\tan60^\circ=\frac{\sin60^\circ}{\cos60^\circ}=\dfrac{\sqrt3/2}{1/2}\) [1 mark]
\(=\sqrt3\), as required. [1 mark]
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