Description

In this topic, we explore much of the fundamental relationships in trigonometry. We explore the concepts of angles in degrees, radians, degrees minutes seconds, and co-terminal angles; the relationships between the trigonometric functions sine, cosine, tangent, secant, cosecant, and cotangent in a right triangle, from the unit circle, and with identities. Next, we exploring graphing trigonometric functions including basic graphs, periods, amplitudes, vertical shifts and phase shifts. We completely explore finding values from the unit circle for the 6 trigonometric functions in radians and degrees by drawing angles and reference angles. We finish by exploreing solving right triangles and their applications to real world scenarios.

Sections of this topic include:

1. Angles

   We start our study of Trigonometry with the study of Angles. Groups in this section include finding coterminal angles; converting angles in degree measure to radian measure; converting angles in radian measure to degree measure; converting angles in radian measure to degree measure in degrees, minutes, and seconds; and converting angles from decimal degrees to degrees, minutes, seconds.

2. The Trigonometric Functions

   In this section, we explore the six trigonometric functions, sine, cosine, tangent, cotangent, secant, and cosecant. We explore these functions in a brief exploration of the unit circle, with identities, and simplifying expressions using identities. Groups in this section include Finding the trigonometric values from the unit circle; determining which quadrant a point lies in given conditions; writing one trigonometric function in terms of another; using identities to find values of trigonometric functions; using identities to write an expression as an integer; wimplifying expressions containing trigonometric functions; and veritifying identities by transforming the left side into the right side.

3. Graphs of Trigonometric Functions

   In this section, we explore how the graphs of trigonometric functions can be used to find exact values. Groups in this section include using evan and odd formulas to find exact values of trigonometric functions; and verifying identities.

    

4. The Trigonometric Functions of Angles

   We apply our knowledge of Trigonometric functions to right triangles to find exact values. This group includes finding the trigonometric values from an ordered pair and right triangle; finding the trigonometric values from an equation; and finding the remaining trigonometric values.

5. The Unit Circle

   In a complete exploration of the 6 trigonometric functions from the unit circle, we investigate how to find the 6 trigonometric functions in various ways for all angles in both degrees and radians from the unit circle. Groups in this section include using special triangles to find the exact values of the 6 trigonometric functions of the unit circle in the first quadrant; finding the exact values of the 6 trigonometric functions for quadrantal angles; finding the exact values of the 6 trigonometric functions for angles in degrees from the unit circle; finding the exact values of the 6 trigonometric functions for angles in radians from the unit circle;finding the exact values of the 6 trigonometric functions for angles in degrees from the unit circle using reference angles;finding the exact values of the 6 trigonometric functions for angles in radians from the unit circle using reference angles; extra practice finding values of the trigonometric functions using reference angles.

6. Trigonometric Graphs

   With a firm foundation of trigonometric values, we next explore the graphs of trigonometric functions including concepts of period, phase shift, vertical shifts, and amplitude. Groups in this section include graphing the sine function; graphing the cosine function.

7. Solving Right Triangles

   A very good application of trigonometry is the application of solving right triangles. Groups in this section include solving a right triangle with exact values; solving a right traingle with a calcualtor; solving a right traingle and representing the answer algebraically.