Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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


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


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

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

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

If $sin(A-B)=\frac { 1 }{ 2 } ,cos(A+B)=\frac { 1 }{ 2 } ,{ 0 }^{ 0 }<A+B\le { 90 }^{ 0 }$ then A =

  1. $15^{ 0 }$
  2. $45^{ 0 }$
  3. $90^{ 0 }$
  4. $30^{ 0 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We have sin(A - B) = 1/2, so A - B = 30 degrees. We also have cos(A + B) = 1/2, so A + B = 60 degrees. Adding these two equations gives 2A = 90 degrees, which means A = 45 degrees.

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

If $(1+\tan 1^{o})(1+\tan 2^{o})(1+\tan 3^{o})....(1+\tan 45^{o})=2^{n}$, then $n$ is equal to 

  1. $21$
  2. $24$
  3. $23$
  4. $22$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pair the terms using the property (1 + tan(theta))(1 + tan(45 - theta)) = 2. Since there are terms from 1 to 44 degrees pairing up to give 2^22, and the term (1 + tan(45)) = 2, the total product is 2^22 * 2 = 2^23, so n = 23.

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 $\sin 10^{\circ}\sin 60^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\sin 60^{\circ}(\sin 10^{\circ}\sin 50^{\circ}\sin 70^{\circ})=\dfrac{\sqrt{3}}{2}\times \dfrac{1}{8}=\dfrac{\sqrt{3}}{16}$

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

$sin^21^0+sin^22^0+sin^23^0+....+sin^290^0$

  1. 0

  2. 1

  3. 89/2

  4. 91/2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the identity sin^2(90 - theta) = cos^2(theta), the sum can be paired from both ends. There are 89 terms from 1 to 89 degrees plus sin^2(90) = 1. Pairing sin^2(theta) + cos^2(theta) gives 44 pairs equal to 1, plus sin^2(45) = 1/2, plus sin^2(90) = 1, totaling 44 + 1/2 + 1 = 91/2.