Trigonometric Identities and Quadrants
The third page delves into important trigonometric identities and the behavior of sine and cosine in different quadrants of the coordinate plane. This information is crucial for understanding circonferenza goniometrica formule.
Definition: Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables.
The page presents the fundamental trigonometric identity:
Highlight: cos²(x) + sin²(x) = 1
This identity is the basis for many trigonometric calculations and proofs. The page also provides formulas for expressing sine in terms of cosine and vice versa:
Example: cos(a) = √(1 - sin²(a))
sin(a) = √(1 - cos²(a))
The concept of quadrants is introduced, showing how the signs of sine and cosine change in each quadrant of the coordinate plane. This is essential for solving trigonometric equations and understanding the behavior of trigonometric functions.
Vocabulary: Quadrant - one of four regions in the coordinate plane, divided by the x and y axes.
The page concludes with an example calculating sin(15°) using the half-angle formula and the known value of sin(30°), demonstrating practical application of trigonometric identities.
Example: sin(15°) = sin(30°/2) = 0.5/2 = 0.25
This comprehensive guide provides a solid foundation for understanding the circonferenza goniometrica seno e coseno, essential for students studying trigonometry and circular functions.
