Mathematics · Quantitative Aptitude

Trigonometric Identities and Values

74 Questions

Trigonometric identities and values questions require evaluating complex angles using standard formulas. These are critical for quantitative aptitude sections in SSC and various state exams. Success depends on memorizing standard values and applying transformation rules.

angle transformationstrigonometric ratiosstandard angle valuessine cosine products

Trigonometric Identities and Values Questions

Multiple choice

What is the value of $\sin 30^\circ$?

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

$\sin 30^\circ = \frac{1}{2}$

Multiple choice

What is the value of $\cos 45^\circ$?

  1. $\frac{1}{2}$
  2. $\frac{\sqrt{3}}{2}$
  3. $\frac{1}{\sqrt{2}}$
  4. $\frac{\sqrt{2}}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\cos 45^\circ = \frac{\sqrt{2}}{2}$

Multiple choice

What is the value of $\tan 60^\circ$?

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

$\tan 60^\circ = \sqrt{3}$

Multiple choice

What is the value of $\cot 30^\circ$?

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

$\cot 30^\circ = \sqrt{3}$

Multiple choice

What is the value of $\sin^{-1} \frac{1}{2}$?

  1. $30^\circ$
  2. $45^\circ$
  3. $60^\circ$
  4. $75^\circ$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\sin^{-1} \frac{1}{2} = 30^\circ$

Multiple choice

What is the value of $\cos^{-1} \frac{\sqrt{2}}{2}$?

  1. $30^\circ$
  2. $45^\circ$
  3. $60^\circ$
  4. $75^\circ$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cos^{-1} \frac{\sqrt{2}}{2} = 45^\circ$

Multiple choice

What is the value of $\tan^{-1} \sqrt{3}$?

  1. $30^\circ$
  2. $45^\circ$
  3. $60^\circ$
  4. $75^\circ$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\tan^{-1} \sqrt{3} = 60^\circ$

Multiple choice

What is the value of cosine of 60 degrees according to Indian mathematicians?

  1. 1/2

  2. √3/2

  3. 1/√2

  4. √2/2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Indian mathematicians, including Aryabhata and Brahmagupta, calculated the value of cosine of 60 degrees to be 1/2.

Multiple choice

What is the value of the expression sec(60°)?

  1. 2

  2. √2

  3. √3

  4. 2√3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The value of the expression sec(60°) is equal to 2.

Multiple choice

What is the value of the expression csc(30°)?

  1. 2

  2. √2

  3. √3

  4. 2√3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The value of the expression csc(30°) is equal to 2.

Multiple choice

What is the value of (sin 30^\circ)?

  1. \(1/2\)
  2. \(\sqrt{3}/2\)
  3. \(1\)
  4. \(0\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that (sin 30^\circ = 1/2).

Multiple choice

What is the value of (cos 60^\circ)?

  1. \(1/2\)
  2. \(\sqrt{3}/2\)
  3. \(0\)
  4. \(-1\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that (cos 60^\circ = 1/2).

Multiple choice

What is the value of the cosine of 60 degrees according to Aryabhata?

  1. 0.5

  2. 0.866

  3. 1

  4. 1.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Aryabhata calculated the cosine of 60 degrees to be 0.5, which is an accurate approximation.

Multiple choice

What is the value of the cosecant of 30 degrees according to Aryabhata?

  1. 0.5

  2. 0.866

  3. 1

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

Aryabhata calculated the cosecant of 30 degrees to be 2, which is an accurate approximation.