際際滷

際際滷Share a Scribd company logo

FUNCIONES CIRCULARES.pptx

Download as PPTX, PDF
Juan Serrano
Juan Serrano

This document provides an overview of circular and periodic functions. It begins by stating the goals of finding trigonometric function values given a point on the unit circle or for special angles. It then defines key terms like unit circle and periodic functions. The document goes on to explain how the unit circle can be used to find exact trigonometric function values for special angles, and provides an example of using a point on the unit circle to find sine and cosine values. It concludes with an example of finding the six trigonometric function values for an angle measuring 5/4 radians.

1 of 9
Download to read offline
6.53 Circular and Periodic Functions Lesson 11.3 Prof. Juan Serrano, MEd.
Circular and Periodic Functions 2 Explore Trigonometric Functions of Special Angles Todays Goals Find value of trigonometric functions given a point on a unit circle or the measure of a special angle. Find values of trigonometric functions that model periodic events. Todays Vocabulary Unit circle Circular functions Periodic functions Cycle Period
Circular and Periodic Functions Learn Circular Functions A unit circle is a circle with a radius of 1 unit centered at the origin on the coordinate plane. Notice that on unit circle, the radian measure of a central angle = 1 or , so the radian measure of an angle is the length of the arc on the unit circle subtended by the angle. You can use a point P on the unit circle to generalize sine and cosine functions by applying the definition of trigonometric functions in right triangles.
FUNCIONES CIRCULARES.pptx
The unit circle is commonly used to show the exact values of and for special angles. The cosine values are the x-coordinates of the point where the terminal sides of the angles intersect the unit circle, and the sine values are the y- coordinates. Circular and Periodic Functions
Example 1: Find Sine and Cosine Given a Point on the Unit Circle The terminal side of in standard position intersects the unit circle at 12 13 , 5 13 . Find and : 12 13 , 5 13 = (, ) = __________ = __________ 12 13 12 13 , 5 13
Example 1: Find Trigonometric Values of Special Angles Find exact values of the six trigonometric functions for an angle that measure 5 4 radians: Using the unit circle, we know that special angle 5 4 intersect the unit circle in Quadrant III at P 2 2 , 2 2 . = _________ = _________
FUNCIONES CIRCULARES.pptx
FUNCIONES CIRCULARES.pptx

More Related Content

FUNCIONES CIRCULARES.pptx

  • 1. 6.53 Circular and Periodic Functions Lesson 11.3 Prof. Juan Serrano, MEd.
  • 2. Circular and Periodic Functions 2 Explore Trigonometric Functions of Special Angles Todays Goals Find value of trigonometric functions given a point on a unit circle or the measure of a special angle. Find values of trigonometric functions that model periodic events. Todays Vocabulary Unit circle Circular functions Periodic functions Cycle Period
  • 3. Circular and Periodic Functions Learn Circular Functions A unit circle is a circle with a radius of 1 unit centered at the origin on the coordinate plane. Notice that on unit circle, the radian measure of a central angle = 1 or , so the radian measure of an angle is the length of the arc on the unit circle subtended by the angle. You can use a point P on the unit circle to generalize sine and cosine functions by applying the definition of trigonometric functions in right triangles.
  • 5. The unit circle is commonly used to show the exact values of and for special angles. The cosine values are the x-coordinates of the point where the terminal sides of the angles intersect the unit circle, and the sine values are the y- coordinates. Circular and Periodic Functions
  • 6. Example 1: Find Sine and Cosine Given a Point on the Unit Circle The terminal side of in standard position intersects the unit circle at 12 13 , 5 13 . Find and : 12 13 , 5 13 = (, ) = __________ = __________ 12 13 12 13 , 5 13
  • 7. Example 1: Find Trigonometric Values of Special Angles Find exact values of the six trigonometric functions for an angle that measure 5 4 radians: Using the unit circle, we know that special angle 5 4 intersect the unit circle in Quadrant III at P 2 2 , 2 2 . = _________ = _________