Geometry is the science created to give understanding and mastery of the external relations of things; to make easy the explanation and description of such relations and the transmission of this mastery.

G.B. Halsted

sections:

      4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, and 4.8

Now we begin our study of trigonometry. The trigonometric functions were first developed referenced to the right triangle; however, by defining these functions in terms of a unit circle, then the functions can be generalized to any angle.

objectives:

• describe angles in standard positions
• measure angles in degrees and degrees, minutes, and seconds
• convert to and from degrees, minutes, and seconds
• draw positive and negative angles
• define complementary and supplementary angles
• measure angles in radians
• convert angles between radians and degrees
• give the length of a circular arc
• relate angular speed to linear speed of a point on a circle
• define the trigonometric functions of sine and cosine and tangent in terms of a right triangle
• define the trigonometric functions of sine and cosine in term of a unit circle
• determine the values of sine and cosine for 30°, 45°, 60°, 90°, and appropriate multiples
• calculate reference angles
• relate the tangent, cosecant, secant, and cotangent to sine and cosine
• give the proper signs for the trigonometric functions in each quadrant
• describe the difference between an ordinary equation and an identity
• write down the pythagorean identity
• use a calculator to compute values for the trigonometric functions
• define an inverse trigonometric function
• use a calculator to compute an inverse sine, cosine, and tangent
• solve for unknown quantities in a right triangle
• apply the trigonometric functions to solve real-life problems
• sketch the graphs of sine and cosine
• state the parity (odd or even) of all the trigonometric functions
• describe the periodicity of the trigonometric functions
• compute the period of a function involving a trigonometric function
• graph a sine or cosine function with a given amplitude, period, and phase shift
• determine the amplitude, period and phase shift from a graph as well as an equation
• graph the tangent, cotangent, secant, and cosecant functions
• apply the trigonometric functions to find unknown quantities in right triangles