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Trigonometry, 2ADV EQ-Bank 5

Find the exact value of

  1. \(\sin 240^{\circ}\)   (1 mark)

  2. \(\tan \left(-120^{\circ}\right)\)   (1 mark)

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a.    \(-\dfrac{\sqrt{3}}{2}\)

b.    \(\sqrt{3}\)

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a.    \(\sin 240^{\circ}=\sin (180+60)=-\sin 60^{\circ}=-\dfrac{\sqrt{3}}{2}\)

b.    \(\tan \left(-120^{\circ}\right)=\tan 240^{\circ}\)

\(\tan 240^{\circ}=\tan (180 + 60)=\tan 60^{\circ}=\sqrt{3}\)

Trigonometry, 2ADV EQ-Bank 4

Find the exact value of

  1. \(\tan 330^{\circ}\)   (1 mark)
  2. \(\cos 510^{\circ}\)   (1 mark)

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a.    \(-\dfrac{1}{\sqrt{3}}\)

b.    \(-\dfrac{\sqrt{3}}{2}\)

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a.    \(\tan 330^{\circ}=\tan (360-30)=-\tan 30^{\circ}=-\dfrac{1}{\sqrt{3}}\)

b.    \(\cos 510^{\circ}=\cos 150^{\circ}\)

\(\cos 150^{\circ}=\cos (180-30)=-\cos 30^{\circ}=-\dfrac{\sqrt{3}}{2}\)

Trigonometry, 2ADV EQ-Bank 3

Find the exact value of

  1. \(\cos \left(-150^{\circ}\right)\)   (1 mark)

  2. \(\sin \, 585^{\circ}\)   (1 mark)

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a.    \(-\dfrac{\sqrt{3}}{2}\)

b.    \(-\dfrac{1}{\sqrt{2}}\)

Show Worked Solution

a.    \(\cos \left(-150^{\circ}\right)=\cos 210^{\circ}\)

\(\cos 210^{\circ}=\cos (180+30)=-\cos 30^{\circ}=-\dfrac{\sqrt{3}}{2}\)
 

b.    \(\sin 585^{\circ}=\sin 225^{\circ}\)

\(\sin 225^{\circ}=\sin (180+45)=-\sin 45^{\circ}=-\dfrac{1}{\sqrt{2}}\)