Tag: trigonometric ratios of some specific angles

Questions Related to trigonometric ratios of some specific angles

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).

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

${\cos}^{2}{73}^{o}+{\cos}^{2}{47}^{o}+\cos{73}^{o}\cos{47}^{o}=.$

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

Using cos^2 A = (1 + cos 2A)/2, the expression becomes (1 + cos 146)/2 + (1 + cos 94)/2 + (cos 146 + cos 94)/2. This simplifies to 1 + (cos 146 + cos 94)/2 + (cos 146 + cos 94)/2 = 1 + cos 146 + cos 94. Using sum-to-product, this results in 3/4.

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

$\dfrac { \cos{ 13 }^{ o }-\sin{ 13 }^{ o } }{ \cos{ 13 }^{ o }+\sin{ 13 }^{ o } } +\dfrac { 1 }{ \cot{ 148 }^{ o } }$ is equal to

  1. $1$
  2. $-1$
  3. $0$
  4. $\dfrac { 1 }{ 2 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\dfrac{\cos 13 - \sin 13}{\cos 13 + \sin 13} + \dfrac{1}{\cot 148}$


$=\dfrac{\cos 13 (1 - \tan 13)}{\cos 13 (1 + \tan 13)} + \dfrac{1}{\cot (180 - 32)}$


$=\dfrac{\tan 45 - \tan 13}{1 + \tan 45 \tan 13} + \dfrac{1}{(-\cot 32)}$

$=\tan (45 - 13) - \tan 32$

$=\tan (32) - \tan 32$

$=0$

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

The value of $\sqrt { 3 } tan{ 10 }^{ 0 }+\sqrt { 3 } tan{ 20 }^{ 0 }+tan{ 10 }^{ 0 }tan{ 20 }^{ 0 }$ is ___________.

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

$\tan (30) = \tan (20 + 10)$


$\dfrac{1}{\sqrt{3}} = \tan 30 = \dfrac{\tan 20 + \tan 10}{1 - \tan 20 \tan 10}$


$1 - \tan 20 \tan 10 = \sqrt{3} (\tan 20 + \tan 10)$

$\sqrt{3} \tan 20 + \sqrt{3} \tan 10 + \tan 10 \tan 20 = 1$