Trigonometry Notes for SSC Exams

Trigonometry gives four to six questions in SSC CGL Tier 1 and many more in Tier 2. The questions are based on standard values, identities and complementary angles, so learning a few tables gives full marks. These trigonometry notes for SSC explain the ratios, the value table and the identities with solved examples and practice questions.

Trigonometric Ratios

In a right triangle with an acute angle theta, the sides are called perpendicular (opposite to theta), base (adjacent to theta) and hypotenuse.

A simple memory aid is "Pandit Badri Prasad Har Har Bole Shankar Har Har": sin = P/H, cos = B/H, tan = P/B.

Standard Value Table

Identities

• sin squared theta + cos squared theta = 1.
• 1 + tan squared theta = sec squared theta.
• 1 + cot squared theta = cosec squared theta.
• tan theta x cot theta = 1, sin theta x cosec theta = 1, cos theta x sec theta = 1.
• Complementary angles: sin (90 - theta) = cos theta, tan (90 - theta) = cot theta, sec (90 - theta) = cosec theta.

Useful Tricks

• If sin theta = p/h, find the base using Pythagoras and then all other ratios.
• sin 60 x cos 30 - cos 60 x sin 30 = 3/4 - 1/4 = 1/2.
• If a question has angles like 20 and 70, 25 and 65, they are complementary, so use the complementary rule.
• If tan A x tan B = 1 and A + B = 90, then tan A = cot B.
• sin theta and cos theta are never more than 1, while sec and cosec are never less than 1.

Typical Trigonometry Question Types in SSC

• Direct value questions using the standard table.
• Questions based on the identity sin squared + cos squared = 1.
• Questions based on complementary angles, such as sin 20 and cos 70.
• Finding the other ratios when one ratio is given.
• Simplifying expressions with secant, cosecant and cotangent.

Most of these can be answered in under 30 seconds if the value table and the three identities are memorised. For the more difficult questions in Tier 2, convert everything into sin and cos and simplify step by step.

Solved Examples

Example 1: Find the value of sin 30 + cos 60.
Solution: sin 30 = 1/2 and cos 60 = 1/2. Sum = 1.

Example 2: If sin theta = 3/5, find cos theta and tan theta.
Solution: Base = square root of (25 - 9) = 4. cos theta = 4/5 and tan theta = 3/4.

Example 3: Find the value of sin 60 x cos 30 - cos 60 x sin 30.
Solution: (root 3 / 2)(root 3 / 2) - (1/2)(1/2) = 3/4 - 1/4 = 1/2.

Example 4: Simplify: (sec squared theta - 1) / tan squared theta.
Solution: sec squared theta - 1 = tan squared theta. So the value is 1.

Example 5: Find the value of sin 25 / cos 65.
Solution: Since 65 = 90 - 25, cos 65 = sin 25. So the value is 1.

Example 6: Find the value of tan 45 x cot 45 + sin squared 30.
Solution: 1 x 1 + 1/4 = 5/4.

Quick Tips to Solve Faster

• Memorise the value table for 0, 30, 45, 60 and 90 degrees.
• Use sin squared + cos squared = 1 to reduce long expressions.
• Look for complementary angles (adding to 90) in every question.
• Convert tan into sin/cos when the expression has mixed ratios.
• Draw the right triangle for questions where one ratio is given.

Common Mistakes to Avoid

• Mixing the values of sin 30 and cos 30.
• Writing 1 + sin squared = cos squared instead of the correct identity.
• Taking tan 90 as 0 instead of undefined.
• Applying the complementary rule to angles that do not add up to 90.
• Forgetting to rationalise the root values in the final answer.

Quick Revision Points

• sin = P/H, cos = B/H, tan = P/B.
• sin squared + cos squared = 1.
• 1 + tan squared = sec squared and 1 + cot squared = cosec squared.
• sin (90 - A) = cos A and tan (90 - A) = cot A.
• sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3 / 2.

Practice Questions With Answers

1. Find the value of sin 45 x cos 45.
   Answer: 1/2 ((1/root 2)(1/root 2)).
2. Find the value of tan 60 x cot 30.
   Answer: 3 (root 3 x root 3).
3. Find the value of sin squared 30 + cos squared 30.
   Answer: 1 (Identity).
4. If tan theta = 1, find theta (0 to 90).
   Answer: 45 degrees (Table).
5. Find the value of cosec 30.
   Answer: 2 (1 / (1/2)).
6. Find the value of sin 70 / cos 20.
   Answer: 1 (Complementary angles).
7. Find the value of 2 sin 30 + 4 cos 60.
   Answer: 3 (1 + 2).
8. Find the value of sec 60.
   Answer: 2 (1 / (1/2)).
9. If sin theta = 5/13, find cos theta.
   Answer: 12/13 (Triplet 5-12-13).
10. Find the value of tan squared 45 + 1.
    Answer: 2 (sec squared 45).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC trigonometry practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Heights and Distances Notes
• Triangle Geometry Notes
• Circle Geometry Notes
• Algebra Formulas Notes
• SSC Trigonometry Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is trigonometry?

Trigonometry is the study of the relations between the angles and the sides of a right triangle.

What are the six trigonometric ratios?

The six ratios are sin, cos, tan, cosec, sec and cot.

What is the value of sin 30 degrees?

sin 30 degrees is 1/2.

What is the basic identity of trigonometry?

sin squared theta + cos squared theta = 1.

What is the complementary angle rule?

sin (90 - A) = cos A, cos (90 - A) = sin A and tan (90 - A) = cot A.

How many trigonometry questions come in SSC CGL Tier 1?

Four to six questions come from trigonometry and heights and distances in most Tier 1 papers.

What is the value of tan 90 degrees?

tan 90 degrees is not defined.

How should I practise trigonometry?

Memorise the table, solve the examples here and attempt the trigonometry practice paper.