Trigonometry is an important maths topic for school exams and quantitative aptitude. It appears in SSC, banking, railway, state exams, entrance exams and placement tests. The topic becomes easy when the meaning, formula and common question types are learned together.
This tutorial explains trigonometry in simple language with definitions, formulas, shortcut tricks, solved examples, practice questions, answers, common mistakes and FAQs. The aim is to help students understand the topic instead of only memorising formulas.
What Is Trigonometry?
Trigonometry is the study of the relation between angles and sides of triangles, especially right-angled triangles.
Important Terms
| Point | Details |
|---|---|
| Hypotenuse | Longest side opposite right angle |
| Perpendicular | Side opposite the angle |
| Base | Side adjacent to the angle |
| Sine | Perpendicular / Hypotenuse |
| Cosine | Base / Hypotenuse |
Important Formulas
| Point | Details |
|---|---|
| sin theta | Perpendicular / Hypotenuse |
| cos theta | Base / Hypotenuse |
| tan theta | Perpendicular / Base |
| tan theta | sin theta / cos theta |
| Identity | sin squared theta + cos squared theta = 1 |
Step-by-Step Method
- Draw or imagine right triangle.
- Mark angle, perpendicular, base and hypotenuse.
- Choose correct ratio.
- Substitute side values.
- Simplify and check range.
Shortcut Tricks
- SOH-CAH-TOA helps remember ratios.
- Hypotenuse is always longest side.
- tan = sin/cos.
- sin 30 = 1/2.
- cos 60 = 1/2.
Common Question Types
| Point | Details |
|---|---|
| Find ratio | Use sides |
| Find side | Use ratio |
| Identity | Simplify expression |
| Standard angle | Use value table |
| Height and distance | Apply triangle relation |
Solved Examples
Example 1
If perpendicular 3 and hypotenuse 5, find sin.
sin = 3/5.
Example 2
If base 4 and hypotenuse 5, find cos.
cos = 4/5.
Example 3
If perpendicular 3 and base 4, find tan.
tan = 3/4.
Example 4
Find sin 30.
sin 30 = 1/2.
Example 5
Find tan 45.
tan 45 = 1.
Government Exam Style Questions
Question 1
In right triangle, sides are 3,4,5. Find all three main ratios for angle opposite side 3.
sin = 3/5, cos = 4/5, tan = 3/4.
Mark sides according to angle.
Question 2
Simplify sin squared A + cos squared A.
It equals 1.
This is the basic identity.
Question 3
If tan A = 1, common acute angle A is?
A = 45 degrees.
Use standard angle values.
Common Mistakes
- Confusing base and perpendicular.
- Using hypotenuse as base.
- Forgetting ratio depends on selected angle.
- Mixing degrees and radians in advanced questions.
- Not learning standard values.
Practice Questions
- sin if P=5 H=13.
- cos if B=12 H=13.
- tan if P=5 B=12.
- sin 30.
- cos 60.
- tan 45.
- sin squared A + cos squared A.
- tan A equals sin A divided by?
- Longest side is?
- Right angle is how many degrees?
Answers to Practice Questions
- 5/13
- 12/13
- 5/12
- 1/2
- 1/2
- 1
- 1
- cos A
- Hypotenuse
- 90
Frequently Asked Questions
What is trigonometry?
It studies sides and angles of triangles.
What is sin?
sin is perpendicular divided by hypotenuse.
What is cos?
cos is base divided by hypotenuse.
What is tan?
tan is perpendicular divided by base.
What is main identity?
sin squared theta plus cos squared theta equals 1.
Revision Notes
Trigonometry starts with right triangle ratios. Mark sides correctly before applying formulas.
For quick revision, write the formula, solve one direct example, and then solve one word problem. This method helps in remembering the concept during exams.
Conclusion
Trigonometry becomes simple when the three main ratios and standard values are clear.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.
Additional Exam Notes
Trigonometry questions should be solved by first writing the known values and then selecting the correct rule. Do not start calculation before checking what the question is asking. Many mistakes happen because students use the correct formula for the wrong quantity.
When practising, solve questions in levels. Start with direct formula use, then move to mixed examples, and finally solve exam-style questions with a timer. This builds accuracy first and speed later.
Always check the final answer. The answer should match the unit, condition and range of the question. A length cannot be negative, an angle should match the triangle condition, and a discount or interest answer should be based on the correct value.