Q1. Evaluate sin30° · cos60° + cos30° · sin60°.
= (½)(½) + (√3/2)(√3/2)
= ¼ + ¾
= 1 (this is sin(30°+60°) = sin90°)
Introduction to Trigonometry — Class 10
Trigonometry is just three ratios of a right triangle. Use the ratio table and calculator, and lock in the identities.
Trigonometric ratiosFor a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Reciprocal ratioscosec = 1/sin, sec = 1/cos, cot = 1/tan.
Standard anglesYou must memorise the values of sin, cos and tan at 0°, 30°, 45°, 60° and 90°.
Identitiessin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ.
Trig ratio table & calculator Interactive
See the standard-angle table, then type any angle to get its sin, cos and tan.
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | ½ | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | ½ | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
sin—
cos—
tan—
Numericals practice Interactive
Standard-angle evaluation with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Pythagorean identity | sin²θ + cos²θ = 1 |
| Secant identity | 1 + tan²θ = sec²θ |
| Cosecant identity | 1 + cot²θ = cosec²θ |
| Ratios | tan θ = sin θ / cos θ |
Common mistakes & exam wins
- Learn the table: sin goes 0, ½, 1/√2, √3/2, 1 for 0°,30°,45°,60°,90°; cos is the reverse.
- tan θ = sin θ / cos θ, so tan90° is undefined (cos90° = 0).
- The identity sin²θ + cos²θ = 1 is the most-used tool — memorise it cold.
- sin(90° − θ) = cos θ and cos(90° − θ) = sin θ (complementary angles).
Frequently asked questions
What are the three basic trigonometric ratios?
sine (opposite/hypotenuse), cosine (adjacent/hypotenuse) and tangent (opposite/adjacent).
What is the value of sin30° and cos60°?
Both equal ½.
What is the fundamental trigonometric identity?
sin²θ + cos²θ = 1, true for every angle θ.