Tag: understanding ratios

Quizzes (0) Questions (37)

Questions Related to understanding ratios

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

The points of discontinuity of $\tan{x}$ are

  1. $n\pi ,n\in I$
  2. $2n\pi ,n\in I$
  3. $(2n+1)\cfrac { \pi }{ 2 } ,n\in I$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $f(x)=\tan {x}$
The points of discontinuity of $f(x)$ are those points where $\tan {x}$ is infinite. This gives
$\tan { x } =\infty $
ie $\tan { x } =\tan { \cfrac { \pi  }{ 2 }  } $
$x=\left( 2n+1 \right) \cfrac { \pi  }{ 2 } ,n\in I$

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

Find the name of the person who first produce a table for solving a triangle's length and angles.

  1. William Rowan Hamilton

  2. Hipparchus

  3. Euclid

  4. Issac Newton
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\text {Hipparchus}$ gave the first table of chords analogus to modern table of sine values, and used them to solve trigonometric problems

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

What is the value of $\sqrt {2}\sec 45^{\circ} - \tan 30^{\circ}$?

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

$\sqrt {2}\sec 45^{\circ} - \tan 30^{\circ} = \sqrt {2}\times \sqrt {2} - \dfrac {1}{\sqrt {3}} = \dfrac {2\sqrt {3} - 1}{\sqrt {3}}$.

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

In triangle $XYZ$, $XZ=YZ$. If the measure of angle $Z$ has ${a}^{o}$, how many degrees are there in the measure of angle $X$?

  1. $x^o=\dfrac {180^o-2a}{2}$
  2. ${ x }^{ o }=\cfrac { { 180 }^{ o }-{ a }^{ o } }{ 2 } $
  3. $x^o=\dfrac {180^o-3a}{3}$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $XZ=YZ$ which implies angles $ZXY$ and $ZYX$ are equal and let it be $\theta$.
We have $ZXY+ZYX+XZY = 180$ , which implies $\theta+\theta+a=180$
Which implies $\theta =\dfrac { (180-a)}{2}$

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

If $\tan A = \dfrac {1 - \cos B}{\sin B}$, then the value of $\dfrac {2\tan A}{1 - \tan^{2}A}$ is

  1. $\dfrac {(\tan B)}{2}$
  2. $2\tan B$
  3. $\tan B$
  4. $4\tan B$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\tan A =  \dfrac {1 - \cos B}{\sin B} $


                       $= \dfrac {2\sin^{2}\dfrac {B}{2}}{2\sin \dfrac {B}{2}\cdot \cos \dfrac {B}{2}}$


                       $= \tan \dfrac {B}{2}$

Therefore, $A = \dfrac {B}{2} \Rightarrow 2A = B$

Now $\dfrac {2\tan A}{1 - \tan^{2}A} = \tan 2A = \tan B$

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

The value of sin $15^0$ is

  1. $\dfrac{\sqrt{3}+1}{2}$
  2. $\dfrac{\sqrt{3}+1}{2\sqrt{2}}$
  3. $\dfrac{-(\sqrt{3}+1)}{2\sqrt{2}}$
  4. $\dfrac{\sqrt{3}-1}{2\sqrt{2}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\sin15^o$


$=\sin(45^o-30^o)$

$=\sin45^o \ \cos30^o - \cos45^o \ \sin30^o$

$=\dfrac{1}{\sqrt{2}} \cdot \dfrac{\sqrt{3}}{2}-\dfrac{1}{\sqrt{2}} \cdot \dfrac{1}{2}$

$=\dfrac{\sqrt{3}-1}{2\sqrt{2}}$
Hence answer is D