In Class 11, trigonometric functions are introduced as a continuation of the study of trigonometry from earlier classes. Here’s a summary of the key points covered in trigonometric functions for Class 11:
1. **Basic Trigonometric Functions**: The primary trigonometric functions studied in Class 11 are sine, cosine, and tangent, which are defined in relation to the sides of a right-angled triangle. These functions are defined as ratios of the sides of a right triangle:
– Sine (sinθ) = Opposite / Hypotenuse
– Cosine (cosθ) = Adjacent / Hypotenuse
– Tangent (tanθ) = Opposite / Adjacent
2. **Trigonometric Identities**: Several important trigonometric identities are introduced, including:
– Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ
– Reciprocal identities: cscθ = 1/sinθ, secθ = 1/cosθ, cotθ = 1/tanθ
– Co-function identities: sin(π/2 – θ) = cosθ, cos(π/2 – θ) = sinθ, tan(π/2 – θ) = cotθ, cot(π/2 – θ) = tanθ, sec(π/2 – θ) = cscθ, csc(π/2 – θ) = secθ
3. **Graphs of Trigonometric Functions**: The graphs of sine, cosine, and tangent functions are studied, including their periods, amplitudes, and general shapes.
4. **Trigonometric Equations**: Basic trigonometric equations are introduced, and methods for solving them are discussed. This includes equations involving sine, cosine, and tangent functions.
5. **Inverse Trigonometric Functions**: The concept of inverse trigonometric functions (such as arcsine, arccosine, and arctangent) is introduced, along with their domains and ranges.
Understanding trigonometric functions is important not only for further studies in mathematics but also for their applications in physics, engineering, and many other fields.
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