Trigonometry Tricks: Ratios, Identities, Height and Distance Questions for SSC CGL, CHSL

Trigonometry carries about 3 to 5 questions in SSC CGL maths, and most of them use only the values of the standard angles and 3 identities. These trigonometry tricks for SSC explain the ratios, the table of standard angles, the identities, the complementary angle rule and the method for height and distance questions, with solved examples.

Trigonometric Ratios

Memory trick: SOH-CAH-TOA.

Table of Standard Angles

Identities

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
• sin(90° − θ) = cos θ and tan(90° − θ) = cot θ

Height and Distance

• The angle of elevation is the angle above the horizontal line when you look up at an object.
• The angle of depression is the angle below the horizontal line when you look down.
• Draw a right-angled triangle, mark the known angle and the side, and use tan θ = height / distance in most questions.

Solved Examples

Example 1. Find the value of sin 30° + cos 60°.
1/2 + 1/2 = 1.

Example 2. If sin θ = 3/5, find cos θ.
cos θ = √(1 − 9/25) = √(16/25) = 4/5.

Example 3. Find the value of tan 45° × sin 90°.
1 × 1 = 1.

Example 4. Find sin 25° − cos 65°.
cos 65° = sin(90 − 65) = sin 25°. So the value is 0.

Example 5 (height and distance). The angle of elevation of the top of a tower from a point 20 m from its base is 45°. Find the height.
tan 45° = height/20, so the height = 20 m.

Example 6. The angle of elevation of the top of a pole from a point 10√3 m from its base is 30°. Find the height.
tan 30° = h/(10√3), so h = 10√3 × 1/√3 = 10 m.

Quick Tips

• Learn the standard angle table by the pattern: sin goes 0, 1/2, 1/√2, √3/2, 1.
• Cos is the reverse of the sin row.
• Use complementary angles to simplify sin and cos pairs.
• Always draw the triangle for height and distance.

Quick Revision Points

• sin² + cos² = 1.
• tan 45° = 1 and sin 30° = 1/2.
• sin(90 − θ) = cos θ.
• tan θ = height/distance in a right triangle.
• The angle of elevation is above the horizontal line.

Practice Questions With Answers

1. Find the value of sin 30°.
   Answer: 1/2
2. Find the value of cos 60°.
   Answer: 1/2
3. Find the value of tan 45°.
   Answer: 1
4. If sin θ = 3/5, find cos θ.
   Answer: 4/5
5. Find the value of sin²30° + cos²30°.
   Answer: 1
6. Find the value of sin 25° − cos 65°.
   Answer: 0
7. Find the value of sec 0°.
   Answer: 1
8. The angle of elevation from a point 20 m from the base of a tower is 45°. Find the height.
   Answer: 20 m
9. Find the value of cos 90°.
   Answer: 0
10. Find the value of tan 60°.
    Answer: √3

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Number System Tricks and the next topic Mensuration Tricks. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes. Also read the Algebra and Trigonometry Formula Guide.

Frequently Asked Questions

What are the six trigonometric ratios?

sin, cos, tan, cosec, sec and cot.

What is SOH-CAH-TOA?

It is a trick: sin = opposite/hypotenuse, cos = adjacent/hypotenuse and tan = opposite/adjacent.

What is the value of sin 30 degrees?

It is 1/2.

What is the value of tan 45 degrees?

It is 1.

What is the main trigonometric identity?

sin squared plus cos squared equals 1.

What is the angle of elevation?

It is the angle above the horizontal when you look up at an object.

What is the angle of depression?

It is the angle below the horizontal when you look down.

How do I solve a height and distance question?

Draw the right triangle, and use tan of the angle equal to height divided by distance.

What is the relation of sin and cos of complementary angles?

sin(90 − θ) = cos θ.

Is trigonometry asked in SSC exams?

Yes. Trigonometry is asked in SSC CGL and CHSL maths.

What are the common mistakes?

Wrong values in the table and mixing up the angle of elevation and depression.

How can I learn the table?

Use the pattern of 0, 1, 2, 3, 4 under the root, divided by 2.