Trigonometry — Study Notes for CG TET Paper II

Overview

Trigonometry forms a crucial component of the Mathematics and Science section in CG TET Paper II, which targets teachers for classes VI to VIII. This topic builds the foundation for understanding relationships between angles and sides of triangles, with direct applications in geometry, mensuration, and real-world problem-solving.

For CG TET, you must master the six trigonometric ratios, their relationships in right-angled triangles, standard angle values, and fundamental identities. Questions typically test your ability to calculate ratios from given information, simplify expressions using identities, and apply complementary angle relationships. A solid grasp of this topic also strengthens your ability to teach spatial reasoning and mathematical relationships to upper primary students.

The scope is limited to right-angled triangle trigonometry and algebraic identities—no trigonometric equations, heights and distances applications, or graphs are expected at this level.

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Key Concepts

• **Trigonometric ratios are defined only for acute angles in a right-angled triangle**, using the relationship between the sides relative to a specific angle (not the right angle).

• **The three primary ratios** — sine, cosine, and tangent — along with their reciprocals (cosecant, secant, cotangent) form the complete set of six ratios.

• **SOH-CAH-TOA memory aid**: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

• **Reciprocal relationships**: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ. These are not new ratios but inverses of the primary three.

• **Complementary angle property**: For any acute angle θ, sin θ = cos(90° - θ), tan θ = cot(90° - θ), sec θ = cosec(90° - θ). This means ratios of complementary angles are related.

• **Pythagorean identities** connect the ratios algebraically and are derived from the Pythagoras theorem applied to unit relationships.

• **Standard angles (0°, 30°, 45°, 60°, 90°)** have fixed ratio values that must be memorised — these appear in nearly every calculation-based question.

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Formulas / Key Facts

### Six Trigonometric Ratios (for angle θ in right triangle) | Ratio | Formula | Reciprocal | |-------|---------|------------| | sin θ | Opposite / Hypotenuse | cosec θ = Hypotenuse / Opposite | | cos θ | Adjacent / Hypotenuse | sec θ = Hypotenuse / Adjacent | | tan θ | Opposite / Adjacent | cot θ = Adjacent / Opposite |

### Quotient Relations