Trigonometric Identities and Equations
This page delves deeper into trigonometric identities and equations, building upon the concepts introduced in the unit circle. It presents fundamental trigonometric identities and demonstrates their application in solving equations.
Definition: For any real number x, cos²x + sin²x = 1. This is known as the Pythagorean identity.
The page begins by stating key properties of sine and cosine functions, which are essential for solving trigonométrie exercices corrigés PDF 1ère S trigonometryexerciseswithsolutionsPDFforfirst−yearsciencestudents.
Highlight: The range of sine and cosine functions is limited: -1 ≤ cos x ≤ 1 and -1 ≤ sin x ≤ 1.
These range limitations are crucial for understanding the behavior of trigonometric functions and are often used in solving equations and inequalities.
The page then provides a detailed example of solving a trigonometric equation:
Example: Solve the equation cos x = -√3/2 for x in the interval −π,0 ∪ −π/2,3π/2.
This example demonstrates the step-by-step process of solving a trigonometric equation, including:
- Identifying the quadrant based on the given interval
- Using the unit circle to find the reference angle
- Applying symmetry principles to find all solutions within the given interval
This problem-solving approach is typical of what students might encounter in trigonométrie pour les nuls pdf trigonometryfordummiesPDF or more advanced cours et exercices corrigés de trigonométrie PDF trigonometrycoursesandsolvedexercisesPDF.
The page concludes with the solution, showing that x = 5π/6 satisfies the equation within the given interval. This type of detailed solution is invaluable for students practicing with trigonométrie première pdf first−yeartrigonometryPDF materials.
