Class 10 Mathematics: Introduction to Trigonometry

How this worksheet helps your child

• Builds confidence in core Mathematics concepts taught in Class 10 through repeated, varied practice.
• Aligned to CBSE and NCERT — questions mirror the pattern children see in school tests and unit assessments.
• Comes with an answer key so parents and students can self-check in minutes, without needing a teacher.
• Pitched at easy level — use it for daily homework, weekend revision or quick exam warm-ups.

About this worksheet

Welcome to our practice worksheet for Class 10 Mathematics, focusing on the fundamental concepts of Introduction to Trigonometry. This essential topic lays the groundwork for understanding relationships between angles and lengths in triangles, a skill that extends far beyond the classroom into fields like engineering, physics, and even architecture. Designed specifically for CBSE Class 10 students, this worksheet is an excellent resource for anyone looking to solidify their understanding of basic trigonometric ratios. It helps students master the initial concepts of trigonometry, particularly how to work with acute angles within a right-angled triangle. Whether your child is just beginning their journey with trigonometry or needs extra practice to build confidence, this easy-difficulty worksheet provides clear, straightforward exercises to ensure a strong grasp of these crucial mathematical principles. It aligns perfectly with the NCERT curriculum, making it an ideal companion for regular study and exam preparation.

What your child will learn

• Identify the sides of a right-angled triangle relative to a given acute angle.
• Define the six basic trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent).
• Calculate the trigonometric ratios for specific acute angles in a right-angled triangle.
• Apply trigonometric ratios to solve simple problems involving right-angled triangles.
• Recognise the relationships between different trigonometric ratios.

Understanding the concept

Trigonometry, at its core, is the study of the relationship between the sides and angles of triangles. For Class 10, we primarily focus on right-angled triangles. A right-angled triangle has one angle that measures exactly 90 degrees. The sides of this special triangle are given names based on their position relative to one of the acute (less than 90 degrees) angles we are considering. The longest side, always opposite the 90-degree angle, is called the 'hypotenuse'. The side directly opposite the acute angle we are looking at is the 'opposite side', and the side next to it (that isn't the hypotenuse) is the 'adjacent side'. Trigonometric ratios are simply fractions that compare the lengths of these sides. The three main ratios are sine (sin), cosine (cos), and tangent (tan). We remember them with the acronym SOH CAH TOA: SOH: Sine = Opposite / Hypotenuse CAH: Cosine = Adjacent / Hypotenuse TOA: Tangent = Opposite / Adjacent There are also three reciprocal ratios: cosecant (cosec = 1/sin), secant (sec = 1/cos), and cotangent (cot = 1/tan). For example, if you have a right-angled triangle where the side opposite an angle is 3 units, the adjacent side is 4 units, and the hypotenuse is 5 units, then the sine of that angle would be 3/5, the cosine would be 4/5, and the tangent would be 3/4. These ratios remain constant for a given angle, regardless of the size of the right-angled triangle.

Tips for parents & teachers

• Encourage your child to label the 'opposite', 'adjacent', and 'hypotenuse' sides clearly for each problem.
• Review the definitions of sine, cosine, and tangent using the SOH CAH TOA mnemonic before your child starts the worksheet.
• Work through the first few problems together to ensure your child understands how to set up the ratios correctly.
• Suggest using different colored pens to highlight the angle in focus and its corresponding sides.
• After completing the worksheet, discuss any questions they found challenging and review the basic concept again.

Topics covered

How to use this worksheet at home

Open the print view and use your browser's Print dialog to print on regular A4 paper or save as a PDF. Hand the printed sheet to your child (Class 10) and set a relaxed time limit — 15 to 25 minutes works for most Mathematics worksheets. When they're done, open the "With answer key" view and let them self-mark question by question. Re-print as many times as you need; the file never expires and there's no download limit.

Frequently asked questions

Is this Mathematics worksheet really free?

Yes — every workbook on WorkbookWala is 100% free to download and print. No login, no email, no paywall. We're free for students, parents and teachers.

Is it aligned to the CBSE / NCERT syllabus?

Yes. All Class 10 worksheets are built around the CBSE and NCERT pattern so they map cleanly to what your child is studying in school.

Can I print this worksheet at home?

Yes. Click "Open print view" and use your browser's Print dialog to print on standard A4 paper, or save it as a PDF for later. The layout is designed to fit cleanly without scaling.

Does it include an answer key?

Yes — click "With answer key" to print a version with answers included, so parents and students can self-mark in minutes.