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Class 10 Introduction to Trigonometry: cheat sheet
CBSE Mathematics. Ratios of the sides of a right-angled triangle, their values at standard angles, the three identities, and heights and distances.
Key ideas
- For an acute angle A in a right triangle: sin A = opposite ÷ hypotenuse, cos A = adjacent ÷ hypotenuse, tan A = opposite ÷ adjacent.
- tan A = sin A ÷ cos A; cosec, sec and cot are the reciprocals of sin, cos and tan.
- The values depend only on the angle, not on the size of the triangle.
- sin A and cos A are never more than 1 for an acute angle; tan 90° is not defined.
- The angle of elevation is measured up from the horizontal; the angle of depression is measured down from the horizontal.
- In heights and distances, draw the right triangle first and mark the side you know and the side you want.
Remember
| Standard values | sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1 |
| cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, cos 90° = 0 | |
| tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3 | |
| Identities | sin²A + cos²A = 1; 1 + tan²A = sec²A; 1 + cot²A = cosec²A |
Watch out
- Taking tan 90° as a number (it is not defined).
- Mixing up the angles of elevation and depression.
- Reading sin²A as sin(A²): it means (sin A)².
Worked example
If cot θ = 20/21, evaluate ((1 + sin θ)(1 − sin θ)) ÷ ((1 + cos θ)(1 − cos θ)).
Working: = (1 − sin² θ)/(1 − cos² θ) = cos² θ/sin² θ = cot² θ = 400/441
Answer: 400/441
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