Mathematics

Eleven Standard

Test your understanding of this lesson Trigonometric ratios of angle 54 degrees:-

1)
The numerical value of \(\cot\frac{\pi}{8}-\tan\frac{\pi}{8}\) is
  • 1
  • -1
  • 2
  • -2
2)
If \(\sin \theta=-\frac{5}{13}\) and \(180^{o}<\theta<270^{o}\), then the value of \(\cos \frac{\theta}{2}\) is
  • -\frac{1}{\sqrt{26}}
  • \frac{1}{\sqrt{26}}
  • \frac{1}{\sqrt{13}}
  • -\frac{1}{\sqrt{13}}
3)
The numerical value of \(\tan\frac{\pi}{3}+2\tan\frac{2\pi}{3}+4\tan\frac{4\pi}{3}+8\tan\frac{8\pi}{3}\) is
  • \(4\sqrt{3}\)
  • \(\frac{4}{\sqrt{3}}\)
  • \(\frac{5}{\sqrt{3}}\)
  • -\(\frac{5}{\sqrt{3}}\)
4)
The value of \(\sin 54^o\) is
  • \(\frac{\sqrt{5}-1}{4}\)
  • \(\frac{\sqrt{5}+1}{4}\)
  • \(\frac{\sqrt{5}+1}{2}\)
  • \(\frac{\sqrt{5}-1}{2}\)
5)
The value of \(\cos 54^o\) is
  • \(\frac{1}{4}\sqrt{10-2\sqrt{5}}\)
  • \(\frac{1}{4}\sqrt{10+2\sqrt{5}}\)
  • \(\frac{1}{4}\Big(\sqrt{5}+1\Big)\)
  • \(\frac{1}{4}\Big(\sqrt{5}-1\Big)\)

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