Tag: trigonometry

Quizzes (11) Questions (86)

Questions Related to trigonometry

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

The value of $\tan 7\dfrac{1}{2}^{o}$ is equal to

  1. $\sqrt{6}+\sqrt{3}+\sqrt{2}-2$
  2. $\sqrt{6}-\sqrt{3}+\sqrt{2}-2$
  3. $\sqrt{6}-\sqrt{3}+\sqrt{2}+2$
  4. $\sqrt{6}-\sqrt{3}-\sqrt{2}-2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula tan(x/2) = sqrt((1-cos x)/(1+cos x)) with x = 15 degrees, or using the half-angle identity for 7.5 degrees, the value is sqrt(6) + sqrt(3) + sqrt(2) - 2.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

$\left( 1-\dfrac { \cos { 61^{o} }  }{ \cos { 1^{o} }  }  \right) \left( 1-\dfrac { \cos { 62^{o} }  }{ \cos { 2^{o} }  }  \right) \left( 1-\dfrac { \cos { 63^{o} }  }{ \cos { 3^{o} }  }  \right) .......\left( 1-\dfrac { \cos { 119^{o} }  }{ \cos { 59^{o} }  }  \right) $

  1. $-1$
  2. $1$
  3. $2$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a telescoping product. Each term (1 - cos(60+x)/cos(x)) simplifies to (cos x - cos(60+x))/cos x = (2 sin(60/2 + x) sin(60/2))/cos x. The product eventually cancels out to -1.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

The value of $\tan \theta .\tan (\theta +60^{o})+\tan \theta \tan (\theta -60^{o})+\tan (\theta +60^{o}).\tan (\theta -60^{o})+3$ is  

  1. $0$
  2. $1$
  3. $-1$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the identity tan(A)tan(B)tan(C) = tan(A+B+C) - (tan A + tan B + tan C) or expanding the terms, the expression simplifies to 0.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

The value of expression $\dfrac { 2\left( \sin{ 1 }^{ o }+\sin{ 2 }^{ o }+\sin{ 3 }^{ o }+.....+\sin{ 89 }^{ o } \right)  }{ 2\left( \cos{ 1 }^{ o }+\cos{ 2 }^{ o}+......+\cos{ 44 }^{ o } \right) +1 }$ equals

  1. $\sqrt{2}$
  2. $1/\sqrt{2}$
  3. $1/2$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The numerator is a sum of sines from 1 to 89, which equals cot(1/2) * sin^2(45). The denominator simplifies similarly. The ratio evaluates to sqrt(2).