Tag: trigonometric identities

Quizzes (1) Questions (68)

Questions Related to trigonometric identities

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

Choose the correct option for the following statement.

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

  1. The given statement is true

  2. The given statement is false

  3. Incomplete information

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

By definition,

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
Therefore, the given statement is true.

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

General solution of $cotx+tanx=2cosecx$ is

  1. $2n\pi\pm\dfrac{2\pi}{3},n\inZ$
  2. $2n\pi\pm\dfrac{4\pi}{3},n\in Z$
  3. $2n\pi\pm\dfrac{5\pi}{3},n\in Z$
  4. $2n\pi\pm\dfrac{\pi}{3},n\in Z$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rewrite the equation cot(x) + tan(x) = 2 csc(x) in terms of sine and cosine: (cos(x)/sin(x)) + (sin(x)/cos(x)) = 2 / sin(x). Simplifying the left side gives 1 / (sin(x)cos(x)) = 2 / sin(x), which leads to cos(x) = 1/2 for sin(x) not equal to 0. Solving cos(x) = 1/2 yields x = 2n pi plus or minus pi/3.

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

If $\tan \theta =\dfrac {\cos 9^{o}+\sin 9^{o}}{\cos 9^{o}-\sin 9^{o}}$, then the value of $\theta$ is

  1. $9^{o}$
  2. $54^{o}$
  3. $18^{o}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Divide numerator and denominator by cos(9 degrees) to get tan(theta) = (1 + tan(9 degrees)) / (1 - tan(9 degrees)) = tan(45 degrees + 9 degrees) = tan(54 degrees). Thus, theta = 54 degrees.

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 $\sin 75^{o}$ is

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

Express sin(75 degrees) as sin(45 degrees + 30 degrees). Using the sine addition formula, sin(45)cos(30) + cos(45)sin(30) = (1/sqrt(2))(sqrt(3)/2) + (1/sqrt(2))(1/2) = (sqrt(3) + 1) / (2 * sqrt(2)).