Free NCERT Solutions, Notes & MCQs for Class 9–12

INTRODUCTION TO TRIGONOMETRY - MCQs

🎯 Knowledge Check

Maths — INTRODUCTION TO TRIGONOMETRY

50 Questions Class 10 MCQs

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

a a. 1 b b. \(\frac{1}{2}\) c c. \(\frac{\sqrt{3}}{2}\) d d. 0

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

a a. 1 b b. \(\frac{1}{2}\) c c. \(\frac{\sqrt{3}}{2}\) d d. 0

What is the value of \(\tan 45^\circ\)?

a a. 0 b b. 1 c c. \(\sqrt{3}\) d d. \(\frac{1}{\sqrt{3}}\)

Which ratio equals \(\sin \theta\)?

a a. \(\frac{\text{Opp}}{\text{Hyp}}\) b b. \(\frac{\text{Adj}}{\text{Hyp}}\) c c. \(\frac{\text{Opp}}{\text{Adj}}\) d d. \(\frac{\text{Hyp}}{\text{Opp}}\)

Which ratio equals \(\cos \theta\)?

a a. \(\frac{\text{Opp}}{\text{Hyp}}\) b b. \(\frac{\text{Adj}}{\text{Hyp}}\) c c. \(\frac{\text{Opp}}{\text{Adj}}\) d d. \(\frac{\text{Hyp}}{\text{Opp}}\)

What is \(\tan 90^\circ\)?

a a. 0 b b. 1 c c. Undefined d d. \(\infty\)

What is the value of \(\sin 0^\circ\)?

a a. 0 b b. 1 c c. \(\frac{1}{2}\) d d. \(\frac{\sqrt{3}}{2}\)

What is \(\cos 0^\circ\)?

a a. 1 b b. 0 c c. \(\frac{\sqrt{2}}{2}\) d d. \(\frac{1}{2}\)

What is \(\tan 0^\circ\)?

a a. 1 b b. 0 c c. Undefined d d. \(\sqrt{3}\)

What is \(\sec \theta\)?

a a. \(\frac{1}{\tan \theta}\) b b. \(\frac{1}{\cos \theta}\) c c. \(\frac{1}{\sin \theta}\) d d. \(\frac{1}{\cot \theta}\)

What is \(\text{cosec }\theta\)?

a a. \(\frac{1}{\sin \theta}\) b b. \(\frac{1}{\cos \theta}\) c c. \(\frac{1}{\tan \theta}\) d d. \(\frac{1}{\cot \theta}\)

What is \(\cot \theta\)?

a a. \(\frac{1}{\tan \theta}\) b b. \(\frac{\sin \theta}{\cos \theta}\) c c. \(\frac{1}{\sin \theta}\) d d. \(\frac{\cos \theta}{\sin \theta}\)

The identity \(\sin^2\theta + \cos^2\theta = ?\)

a a. \(\sin \theta\) b b. \(\cos \theta\) c c. 1 d d. \(\sec \theta\)

\(1 + \tan^2\theta = ?\)

a a. \(\cos^2\theta\) b b. \(\sec^2\theta\) c c. \(\text{cosec}^2\ \theta\) d d. \(\sin^2\theta\)

What is \(\sin 45^\circ\)?

a a. \(\frac{1}{2}\) b b. \(\frac{\sqrt{3}}{2}\) c c. \(\frac{\sqrt{2}}{2}\) d d. 1

What is \(\cos 90^\circ\)?

a a. 1 b b. 0 c c. \(-1\) d d. \(\frac{\sqrt{2}}{2}\)

What is \(\tan 60^\circ\)?

a a. 1 b b. \(\sqrt{3}\) c c. \(\frac{1}{\sqrt{3}}\) d d. 0

What is \(\cot 45^\circ\)?

a a. 1 b b. 0 c c. \(\sqrt{3}\) d d. \(\frac{1}{\sqrt{3}}\)

What is \(\sec 60^\circ\)?

a a. 2 b b. \(\frac{1}{2}\) c c. \(\sqrt{3}\) d d. \(\frac{2}{\sqrt{3}}\)

What is \(\text{cosec }30^\circ\)?

a a. 1 b b. 2 c c. \(\sqrt{3}\) d d. \(\frac{1}{2}\)

\(\sin(90^\circ - \theta) = ?\)

a a. \(\cos \theta\) b b. \(\sin \theta\) c c. \(\tan \theta\) d d. \(\cot \theta\)

\(\cos(90^\circ - \theta) = ?\)

a a. \(\sin \theta\) b b. \(\tan \theta\) c c. \(\cot \theta\) d d. \(\sec \theta\)

\(\tan(90^\circ - \theta) = ?\)

a a. \(\sec \theta\) b b. \(\cot \theta\) c c. \(\tan \theta\) d d. \(\cos \theta\)

If \(\sin \theta = \frac{3}{5}\), then \(\cos \theta = ?\)

a a. \(\frac{3}{5}\) b b. \(\frac{4}{5}\) c c. \(\frac{\sqrt{5}}{3}\) d d. \(\frac{5}{3}\)

If \(\cos \theta = \frac{12}{13}\), then \(\sin \theta = ?\)

a a. \(\frac{12}{13}\) b b. \(\frac{5}{13}\) c c. \(\frac{13}{12}\) d d. \(\frac{1}{13}\)

If \(\tan \theta = \frac{3}{4}\), then \(\sec \theta = ?\)

a a. \(\frac{5}{4}\) b b. \(\frac{5}{3}\) c c. \(\frac{4}{5}\) d d. \(\frac{3}{5}\)

Which equals \(\frac{\text{Hyp}}{\text{Adj}}\)?

a a. \(\sin \theta\) b b. \(\sec \theta\) c c. \(\cot \theta\) d d. \(\text{cosec }\theta\)

What is \(\sin 90^\circ\)?

a a. 0 b b. 1 c c. \(\frac{\sqrt{3}}{2}\) d d. \(\frac{1}{2}\)

What is \(\tan 30^\circ\)?

a a. 1 b b. \(\frac{1}{\sqrt{3}}\) c c. \(\sqrt{3}\) d d. \(\frac{1}{2}\)

If \(\sin \theta\) increases, \(\cos \theta\) ______.

a a. increases b b. decreases c c. stays constant d d. becomes undefined

Which ratio is always \(\le 1\)?

a a. \(\sin \theta\) b b. \(\cos \theta\) c c. Both a & b d d. \(\tan \theta\)

Which is always \(\ge 1\)?

a a. \(\sin \theta\) b b. \(\cos \theta\) c c. \(\sec \theta\) d d. \(\tan \theta\)

If \(\sin \theta = \frac{4}{5}\), then \(\tan \theta = ?\)

a a. \(\frac{3}{4}\) b b. \(\frac{4}{3}\) c c. \(\frac{5}{4}\) d d. \(\frac{1}{3}\)

If \(\tan \theta = 1\), then \(\theta = ?\)

a a. \(0^\circ\) b b. \(30^\circ\) c c. \(45^\circ\) d d. \(90^\circ\)

Which side is opposite the right angle?

a a. Opposite side b b. Adjacent side c c. Hypotenuse d d. None

What is \(\cot 60^\circ\)?

a a. \(\frac{1}{\sqrt{3}}\) b b. \(\sqrt{3}\) c c. 1 d d. 0

What is \(\sec 0^\circ\)?

a a. 0 b b. 1 c c. Undefined d d. 2

What is \(\text{cosec } 90^\circ\)?

a a. 0 b b. 1 c c. Undefined d d. 2

If \(\text{Opp} = 7\), \(\text{Adj} = 24\), then \(\tan \theta = ?\)

a a. \(\frac{7}{24}\) b b. \(\frac{24}{7}\) c c. \(\sqrt{7^2+24^2}\) d d. \(\frac{1}{24}\)

If \(\cos \theta = \frac{4}{5}\), then \(\tan \theta = ?\)

a a. \(\frac{3}{4}\) b b. \(\frac{4}{3}\) c c. \(\frac{5}{3}\) d d. \(\frac{3}{5}\)

What is \(\text{cosec }60^\circ\)?

a a. \(\frac{2}{\sqrt{3}}\) b b. \(\sqrt{3}\) c c. 1 d d. 2

For acute angles, which is always positive?

a a. \(\sin \theta\) b b. \(\cos \theta\) c c. \(\tan \theta\) d d. All of these

\(\sin \theta = \frac{\sqrt{3}}{2}\) for which angle?

a a. \(30^\circ\) b b. \(45^\circ\) c c. \(60^\circ\) d d. \(90^\circ\)

\(\cos^2\theta = 1 - ?\)

a a. \(\sin^2\theta\) b b. \(\cot^2\theta\) c c. \(\tan^2\theta\) d d. \(\sec^2\theta\)

If \(\cot \theta = \frac{5}{12}\), find \(\sin \theta\).

a a. \(\frac{5}{13}\) b b. \(\frac{12}{13}\) c c. \(\frac{13}{12}\) d d. \(\frac{1}{13}\)

\(\sin 45^\circ \times \cos 45^\circ = ?\)

a a. \(\frac{1}{2}\) b b. \(\frac{1}{\sqrt{2}}\) c c. \(\frac{1}{\sqrt{3}}\) d d. \(\frac{\sqrt{3}}{2}\)

Trigonometric ratios depend on:

a a. size of triangle b b. angle of triangle c c. perimeter d d. area

\(\tan \theta \cdot \cot \theta = ?\)

a a. 1 b b. 0 c c. \(\sin \theta\) d d. \(\cos \theta\)

If \(\sin \theta = 1\), then \(\theta = ?\)

a a. \(0^\circ\) b b. \(30^\circ\) c c. \(90^\circ\) d d. \(45^\circ\)

Which identity helps express \(\tan \theta\) in terms of \(\sin\theta, \cos\theta\)?

a a. \(\sin^2\theta + \cos^2\theta = 1\) b b. \(\tan \theta = \frac{\sin \theta}{\cos \theta}\) c c. \(1 + \tan^2\theta = \sec^2\theta\) d d. \(\sin(90^\circ - \theta) = \cos \theta\)

📚

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

Sharing this chapter

Mathematics | Maths Class 10

Mathematics | Maths Class 10 — Complete Notes & Solutions · academia-aeternum.com

🎓 Class 10 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

Share on

X / Twitter

Facebook

academia-aeternum.com/blogs/MCQs/mathematics/X-Class/introduction-to-trigonometry-x-mcqs/ Copy link

💡

Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

Trigonometry is the branch of mathematics that studies the relationship between the sides and angles of a right-angled triangle usin g trigonometric ratios such as sin e, cos in e, and tan gent.

Trigonometric ratios are ratios of the lengths of the sides of a right triangle with respect to one of its acute angles. They include sin , cos , tan , cos ec, sec , and cot .

The six ratios are: sin \(\theta\), cos \(\theta\), tan \(\theta\), cos ec\(\ \theta\), sec \(\theta\), and cot \(\theta\).

sin \(\theta\) = Opposite side ÷ Hypotenuse.

cos \(\theta\) = Adjacent side ÷ Hypotenuse.

tan \(\theta\) = Opposite side ÷ Adjacent side.

tan \(\theta\) = sin \(\theta\) ÷ cos \(\theta\).

cosec\(\ \theta\) = 1 ÷ sin \(\theta\) = Hypotenuse ÷ Opposite side.

sec \(\theta\) = 1 ÷ cos \(\theta\) = Hypotenuse ÷ Adjacent side.

cot \(\theta\) = 1 ÷ tan \(\theta\) = Adjacent side ÷ Opposite side.

Values include: sin 0\(^\circ\)=0, sin 30\(^\circ\)=1/2, sin 45\(^\circ\)=v2/2, sin 60\(^\circ\)=v3/2, sin 90\(^\circ\)=1 (others similarly defined).

They help solve real-life problems involving heights, distan ces, angles of elevation/depression, navigation, physics, engineering, and architecture.

The angle formed between the horizontal line and the line of sight when the observer looks upward at an object.

The angle formed between the horizontal line and the line of sight when the observer looks downward from a higher point.

sin ²\(\ \theta\) + cos ²\(\ \theta\) = 1.

INTRODUCTION TO TRIGONOMETRY - MCQs

Maths — INTRODUCTION TO TRIGONOMETRY

Frequently Asked Questions

Recent Posts

INTRODUCTION TO TRIGONOMETRY – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Let's Connect

INTRODUCTION TO TRIGONOMETRY - MCQs

Maths — INTRODUCTION TO TRIGONOMETRY

Frequently Asked Questions

Q 01 What is trigonometry in simple terms?

Q 02 What is the meaning of trigonometric ratios?

Q 03 What are the six trigonometric ratios for an acute angle?

Q 04 How is sin \(\theta\) defined in a right-angled triangle?

Q 05 How is cos \(\theta\) defined?

Q 06 How is tan \(\theta\) defined?

Q 07 What is the relationship between tan \(\theta\), sin \(\theta\), and cos \(\theta\)?

Q 08 What is cosec\(\ \theta\)?

Q 09 What is sec \(\theta\)?

Q 10 What is cot \(\theta\)?

Q 11 What are the stan dard trigonometric values of 0\(^\circ\), 30\(^\circ\), 45\(^\circ\), 60\(^\circ\), and 90\(^\circ\)?

Q 12 Why are trigonometric ratios importan t?

Q 13 What is an angle of elevation?

Q 14 What is an angle of depression?

Q 15 What is the Pythagorean identity in trigonometry?

Recent Posts

INTRODUCTION TO TRIGONOMETRY – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Let's Connect