Olympiad – Class X – Mathematics - Introduction to Trigonometry

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Question - 1

\(\Delta\)ABC is right angled at A. If AC = 8 cm and AB = 6 cm, what is the value of cosecB?

  • A \(\frac { 5 }{ 4 } \)
  • B \(\frac { 3 }{ 4 } \)
  • C \(\frac { 4 }{ 3 } \)
  • D \(\frac { 4 }{ 5 } \)

Question - 2

\(\Delta\)ABC is right angled at A.lf BC =\(\sqrt { 2 } \) and AB = AC = 1,what is the measure of \(\angle B\)?

  • A 60°
  • B 45°
  • C 30°
  • D 90°

Question - 3

What is the value of \(\theta\) for which tan\(\theta\) = cot\(\theta\)?

  • A 60°
  • B 45°
  • C 90°
  • D 0°

Question - 4

Given sin \(\theta\)+\(\frac { 1 }{ sin\ \theta } \)=4, what is the value of sin2\(\theta\) + \(\frac { 1 }{ { sin }^{ 2 }\theta } \)?

  • A 20
  • B 16
  • C 14
  • D 4

Question - 5

Given tan\(\theta\) \(=\frac { 7 }{ 24 } \), what is the value of sin \(\theta\) + cos \(\theta\)?

  • A \(\frac { 25 }{ 31 } \)
  • B \(\frac { 31 }{ 25 } \)
  • C \(\frac { 24 }{ 25 } \)
  • D \(\frac { 31 }{ 24 } \)

Question - 6

Find the value of cos30° cos45° - sin 30° sin45° .

  • A \(\frac { \sqrt { 6 } +1 }{ 2 } \)
  • B \(\frac { \sqrt { 6 } +\sqrt { 2 } }{ 4 } \)
  • C \(\frac { \sqrt { 6 } -\sqrt { 2 } }{ 8 } \)
  • D \(\frac { \sqrt { 2 } (\sqrt { 3 } -1) }{ 4 } \)

Question - 7

What is the value of tan 7° tan 23° tan 60° tan 67° tan 83°?

  • A \(\frac { 1 }{ \sqrt { 3 } } \)
  • B \(\sqrt { 3 } \)
  • C 1
  • D \(\infty \)

Question - 8

\(\Delta\)ABC is an isosceles triangle with the unequal side measuring 12 cm. If both the equal sides measure 19 cm, what is the measure of \(\angle \)BAC?

  • A 36.8°
  • B 68°
  • C 38°
  • D 60°

Question - 9

ABCD is a trapezium in which AB = 8 cm, AD = 4 cm and CD = 3 cm.
 
What is the length of BC to the nearest whole number?

  • A 5 cm
  • B \(\sqrt { 41 } \) cm
  • C 8 em
  • D 7 cm

Question - 10

The figure shows an isosceles triangle ABC. Find the length of the perpendicular from A to BC.

  • A 5.45 cm
  • B 4.55 cm
  • C 5.6 cm
  • D 4.54 cm
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