basic concepts of trignometry

1. Trigonometric Ratios:

• In a right-angled triangle, there are six trigonometric ratios: sine (sin), cosine (cos),
tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).
• These ratios are defined as follows:
• sinθ = Opposite/Hypotenuse
• cosθ = Adjacent/Hypotenuse
• tanθ = Opposite/Adjacent
• cosecθ = 1/sinθ
• secθ = 1/cosθ
• cotθ = 1/tanθ
2. Pythagorean Identities:

• In a right-angled triangle, the Pythagorean theorem states that the square of the
hypotenuse is equal to the sum of the squares of the other two sides.
• This can be written as: a^2 + b^2 = c^2, where c represents the hypotenuse.
• Using this theorem, we can derive the following trigonometric identities:
• sin^2θ + cos^2θ = 1
• 1 + tan^2θ = sec^2θ
• 1 + cot^2θ = cosec^2θ
3. Trigonometric Functions of Special Angles:

• For certain angles (0°, 30°, 45°, 60°, 90°), the trigonometric ratios have specific
values:
• sin 0° = 0, cos 0° = 1, tan 0° = 0
• sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
• sin 45° = √2/2, cos 45° = √2/2, tan 45° = 1
• sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3
• sin 90° = 1, cos 90° = 0, tan 90° = undefined
4. Trigonometric Identities:

• Trigonometric identities are equations involving trigonometric functions that are
true for all values of the variables.
• Some commonly used identities include:
• Sum and Difference Identities: sin(A ± B), cos(A ± B), tan(A ± B)
• Double Angle Identities: sin(2θ), cos(2θ), tan(2θ)
• Half Angle Identities: sin(θ/2), cos(θ/2), tan(θ/2)
• Pythagorean Identities (mentioned in point 2)