Trigonometry Notes
1. **Basic Trigonometric Ratios** Trigonometry deals with the relationships between the sides and
angles of a right-angled triangle. The basic trigonometric ratios are: - **Sine (sin)**: sin(θ) =
Opposite / Hypotenuse - **Cosine (cos)**: cos(θ) = Adjacent / Hypotenuse - **Tangent (tan)**: tan(θ)
= Opposite / Adjacent - **Cosecant (csc)**: csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite - **Secant
(sec)**: sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent - **Cotangent (cot)**: cot(θ) = 1 / tan(θ) =
Adjacent / Opposite
2. **Trigonometric Identities** - **Pythagorean Identities**: - sin²(θ) + cos²(θ) = 1 - 1 + tan²(θ) =
sec²(θ) - 1 + cot²(θ) = csc²(θ) - **Reciprocal Identities**: - csc(θ) = 1 / sin(θ) - sec(θ) = 1 / cos(θ) -
cot(θ) = 1 / tan(θ) - **Angle Sum and Difference Identities**: - sin(A + B) = sin A * cos B + cos A *
sin B - cos(A + B) = cos A * cos B - sin A * sin B - tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
3. **Trigonometric Values for Special Angles** - For 30°: - sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) =
1/√3 - For 45°: - sin(45°) = √2/2, cos(45°) = √2/2, tan(45°) = 1 - For 60°: - sin(60°) = √3/2, cos(60°) =
1/2, tan(60°) = √3
1. **Basic Trigonometric Ratios** Trigonometry deals with the relationships between the sides and
angles of a right-angled triangle. The basic trigonometric ratios are: - **Sine (sin)**: sin(θ) =
Opposite / Hypotenuse - **Cosine (cos)**: cos(θ) = Adjacent / Hypotenuse - **Tangent (tan)**: tan(θ)
= Opposite / Adjacent - **Cosecant (csc)**: csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite - **Secant
(sec)**: sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent - **Cotangent (cot)**: cot(θ) = 1 / tan(θ) =
Adjacent / Opposite
2. **Trigonometric Identities** - **Pythagorean Identities**: - sin²(θ) + cos²(θ) = 1 - 1 + tan²(θ) =
sec²(θ) - 1 + cot²(θ) = csc²(θ) - **Reciprocal Identities**: - csc(θ) = 1 / sin(θ) - sec(θ) = 1 / cos(θ) -
cot(θ) = 1 / tan(θ) - **Angle Sum and Difference Identities**: - sin(A + B) = sin A * cos B + cos A *
sin B - cos(A + B) = cos A * cos B - sin A * sin B - tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
3. **Trigonometric Values for Special Angles** - For 30°: - sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) =
1/√3 - For 45°: - sin(45°) = √2/2, cos(45°) = √2/2, tan(45°) = 1 - For 60°: - sin(60°) = √3/2, cos(60°) =
1/2, tan(60°) = √3
