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SparkEd Math offers 60+ practice questions for Introduction to Trigonometry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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SparkEd Math uses visual step-by-step solutions for every Introduction to Trigonometry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Introduction to Trigonometry content aligned with the CBSE syllabus?

Yes, all Introduction to Trigonometry questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Introduction to Trigonometry — Class 10 CBSE (2025-26)

About Introduction to Trigonometry — Class 10 CBSE

Define trigonometric ratios, find values of standard angles, and prove trigonometric identities. This topic is part of the CBSE Class 10 mathematics syllabus (chapter: Chapter 8). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Introduction to Trigonometry

Introduction to Trigonometry: The Basics
Trigonometric Ratios: Sine, Cosine, Tangent
Reciprocal Ratios and Inter-relationships
Trigonometric Ratios of Specific Angles
Trigonometric Identities and Summary

Interactive lesson · about 15 minutes · checkpoint question after every unit

Introduction to Trigonometry — solved examples for Class 10 CBSE

Example 1easy

In a right-angled triangle ABC, right-angled at B, if AB = 8 cm and BC = 6 cm, what is the value of tan A?

A)3/4
B)4/3
C)3/5
D)4/5

Step-by-step solution

Identify the sides relative to angle A. The side opposite to angle A is BC = 6 cm. The side adjacent to angle A is AB = 8 cm.
Apply the definition of tan A.
$tan A = Opposite / Adjacent$
Substitute the given values.
$tan A = BC / AB = 6 / 8$
Simplify the fraction.
$tan A = 3 / 4$

Answer: 3/4

Example 2medium

In a right-angled triangle ABC, right-angled at B, if AB = 7 cm and BC = 24 cm, what is the value of sin C?

A)7/25
B)24/25
C)7/24
D)24/7

Step-by-step solution

Given a right-angled triangle ABC, with the right angle at B. AB = 7 cm, BC = 24 cm.
Using the Pythagorean theorem, AC² = AB² + BC².
$AC² = 7² + 24² = 49 + 576 = 625$
So, AC = √625 = 25 cm.
For angle C, the side opposite is AB and the hypotenuse is AC. Therefore, sin C = Opposite/Hypotenuse = AB/AC.
$sin C = 7/25$

Answer: 7/25

Example 3hard

Which of the following statements is NOT possible for an acute angle A?

A)sin A = (p² + 1) / (p² + 2) for some real p
B)sec A = 1/2
C)tan A = 20
D)cos A = (q² - 1) / (q² + 1) for some real q where q ≠ 0

Step-by-step solution

For an acute angle A, 0 < sin A < 1, 0 < cos A < 1, tan A > 0, sec A > 1, cosec A > 1, cot A > 0.
Option A: sin A = (p² + 1) / (p² + 2). Since p² ≥ 0, p² + 1 < p² + 2. So, (p² + 1) / (p² + 2) is always less than 1. Also, since p² + 1 > 0 and p² + 2 > 0, sin A > 0. Thus, 0 < sin A < 1 is possible.
Option B: sec A = 1/2. For an acute angle A, sec A is always greater than 1. Since 1/2 is less than 1, sec A = 1/2 is NOT possible.
Option D: cos A = (q² - 1) / (q² + 1). For this to be a valid cosine value, -1 < cos A < 1. If q=1, cos A = 0. If q>1, 0 < cos A < 1. If 0<q<1, then q²-1 is negative, but q²+1 is positive, so cos A would be negative, which is not possible for an acute angle. However, the question states 'for some real q where q ≠ 0'. If q is real, q²-1 can be negative or positive. But for an acute angle A, cos A must be positive (0 < cos A < 1). If q=1, cos A = 0 (not acute). If q>1, then q²-1 is positive and q²-1 < q²+1, so 0 < cos A < 1, which is possible. Thus, this statement *can* be possible for certain q.

Answer: sec A = 1/2

Practice questions on Introduction to Trigonometry

Q1.easy
Which of the following statements about trigonometric ratios for an acute angle A is ALWAYS true?
1. A)sin A > 1
2. B)sec A < 1
3. C)tan A can be greater than 1
4. D)cos A can be 5/3
Show answer
Answer: tan A can be greater than 1
Hint: Consider the definitions of sin, cos, tan, and sec in terms of sides of a right triangle. Remember that the hypotenuse is always the longest side.
Q2.easy
If sin θ = 12/13, what is the value of cosec θ?
1. A)13/12
2. B)5/12
3. C)12/5
4. D)1/13
Show answer
Answer: 13/12
Hint: Recall the reciprocal relationship between sine and cosecant.
Q3.easy
Evaluate the expression: 2 × sin 30° + tan 45°.
1. A)1
2. B)2
3. C)3/2
4. D)5/2
Show answer
Answer: 2
Hint: Recall the standard trigonometric values for 30° and 45°.
Q4.medium
If 3 cot A = 4, then the value of sin A is:
1. A)4/5
2. B)5/3
3. C)3/5
4. D)4/3
Show answer
Answer: 3/5
Hint: From cot A, you can form a right-angled triangle using the ratio of adjacent to opposite sides. Then use Pythagoras theorem to find the hypotenuse.
Q5.medium
Evaluate: (sin 60° × cos 30° + sin 30° × cos 60°)
1. A)0
2. B)1/2
3. C)1
4. D)√3/2
Show answer
Answer: 1
Hint: Recall the values of sine and cosine for the standard angles 30° and 60°. Substitute these values into the expression and simplify.
Q6.medium
Which of the following statements is INCORRECT?
1. A)sin 0° = 0
2. B)cos 90° = 0
3. C)tan 45° = 1
4. D)sec 0° = 0
Show answer
Answer: sec 0° = 0
Hint: Recall the definitions and standard values of trigonometric ratios for 0° and 90°. Remember that secant is the reciprocal of cosine.
Q7.hard
If (sin θ + cos θ) / (sin θ - cos θ) = 3, then what is the value of sin⁴θ - cos⁴θ?
1. A)1/5
2. B)2/5
3. C)3/5
4. D)4/5
Show answer
Answer: 3/5
Hint: First, use the given equation to find the value of tan θ. Then, express sin⁴θ - cos⁴θ in terms of tan θ or by simplifying it using algebraic identities.
Q8.hard
Evaluate: (cos²20° + cos²70°) / (sec²50° - cot²40°) + 2sin²30° - (1/2)cos²60°.
1. A)1
2. B)2
3. C)2.25
4. D)2.5
Show answer
Answer: 2
Hint: Use complementary angle identities (e.g., cos(90°-A) = sin A, cot(90°-A) = tan A) and fundamental identities like sin²A + cos²A = 1 and sec²A - tan²A = 1. Also, recall the values of standard angles.
Q9.hard
If x = a sin θ and y = b cos θ, which of the following expressions must be true?
1. A)b²x² + a²y² = a²b²
2. B)a²x² + b²y² = a²b²
3. C)x²/a² + y²/b² = 1
4. D)x² + y² = a² + b²
Show answer
Answer: b²x² + a²y² = a²b²
Hint: Rearrange the given equations to express sin θ and cos θ in terms of x, y, a, b. Then use the fundamental identity sin²θ + cos²θ = 1.

These are 9 of the 60 questions available for Introduction to Trigonometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.