Tag: trigonometry

Questions Related to trigonometry

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

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


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


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

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

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

Values of : $sin{ 10 }^{ 0 }sin{ 50 }^{ 0 }sin{ 60 }^{ 0 }sin{ 70 }^{ 0 }$ is

  1. $\cfrac { 3 }{ 16 } $
  2. $\cfrac { 5 }{ 16 } $
  3. $\cfrac { \sqrt { 3 } }{ 16 } $
  4. $\cfrac { \sqrt { 5 } }{ 16 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As we know that

$\sin A\sin(60^{\circ}-A)\sin (60^{\circ}+A)=\dfrac{1}{4}\sin 3 A$
Put $A=10^{\circ}$
So $\sin 10^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\dfrac{1}{4}\sin 30^{\circ}=\dfrac{1}{8}$
So $\sin 10^{\circ}\sin 60^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\sin 60^{\circ}(\sin 10^{\circ}\sin 50^{\circ}\sin 70^{\circ})=\dfrac{\sqrt{3}}{2}\times \dfrac{1}{8}=\dfrac{\sqrt{3}}{16}$