Page 2: Angle Relationships and Inverse Functions

This page details the relationships between angles and introduces inverse trigonometric functions.

Definition: Inverse trigonometric functions (arcsin, arccos, arctan) find the angle when given a trigonometric ratio

Highlight: Key angle relationships:

• sin$-x$ = -sin(x)
• cos$-x$ = cos(x)
• tan$-x$ = -tan(x)

Example: For 45° angles: sin(45°) = cos(45°) = √2/2

Vocabulary: Angular units conversion: 360° = 2π radians

Page 3: Triangle Problem Solving

This page focuses on practical applications and the sine theorem.

Example: A building height problem using angles of elevation (45° and 40°) demonstrates practical trigonometry application

Definition: The sine theorem states that in any triangle, the ratio of the sine of an angle to the length of the opposite side is constant

Highlight: The sine theorem is particularly useful when solving triangles with known angles and at least one known side

Page 4: Cosine Theorem and Triangle Resolution

This page covers the cosine theorem and its applications in triangle resolution.

Definition: The cosine theorem states that a² = b² + c² - 2bc·cos(A)

Example: Detailed solution of a triangle with sides 12 and 9, and an angle of 60°, resulting in the third side being √117

Highlight: The cosine theorem is especially useful when three sides are known or two sides and their included angle

Page 5: Trigonometric Equations

This page explores solving trigonometric equations and includes various exercises.

Highlight: Methods for solving different types of trigonometric equations, including those involving multiple functions

Example: Solution of equation 2cos(x)tan(x) - 1 = 0 through substitution and algebraic manipulation

Vocabulary: Radian measure conversions and relationships to degrees are emphasized throughout exercises

Page 6: Advanced Triangle Problems

This page presents complex triangle problems and their solutions.

Example: Multiple triangle resolution problems involving various combinations of known sides and angles

Highlight: Integration of multiple concepts including sine theorem, cosine theorem, and angle relationships

Definition: The process of solving triangles requires systematic application of appropriate theorems based on given information

Page 1: Fundamental Trigonometric Properties

This page introduces core trigonometric concepts and fundamental relationships. The unit circle with radius 1 and center at origin (0,0) serves as the foundation for understanding trigonometric functions.

Definition: The equation of a circle with center (a,b) and radius r is $x-a$² + $y-b$² = r²

Highlight: The fundamental trigonometric identity cos²(α) + sin²(α) = 1 establishes the relationship between sine and cosine functions

Vocabulary:

• Secant (sec): The reciprocal of cosine
• Cosecant (cosec): The reciprocal of sine
• Cotangent (cotan): The reciprocal of tangent

Example: While sine and cosine are bounded between -1 and 1, tangent can take any real value, approaching infinity at 90° + k·360°