L13. 1 and L13. 2 Obj 1: Students will find period and amplitude L13.1 and L13.2 Obj 1: Students will find period and amplitude. Obj 2: Students will use the unit circle to find values of trig functions. A periodic function repeats a pattern of y- values at regular intervals. One complete pattern is a cycle. The period of a function is the horizontal length of one cycle. The amplitude of a periodic function is half the height of the function.

For the following slides: Is it periodic. If it is periodic a For the following slides: Is it periodic? If it is periodic a. identify one cycle in two different ways b. Find the period c. Find the amplitude

Amplitude: height from middle to top or half the distance from bottom to top Period: from beginning to end of a cycle

1. Find the circumference of a circle whose radius is one foot. 2. Find the circumference of a circle whose radius is 1 meter. 3. Find the circumference of a circle whose radius is one inch. 4. What does SOH CAH TOA stand for?

Sin 30° = opposite/hypotenuse Cos 30° = adjacent/hypotenuse Tan 30° =opposite/hypotenuse n b o c Z a m Sin 30° = Z/Y = c/b = o/n = ½ or .5 Cos 30° = x/y=a/b=m/n= √3 / 2 or .866 Tan 30° = z/x = c/a= o/m= √3 /3 or .577

Find the cosine and sine of 135°. Angles and the Unit Circle Find the cosine and sine of 135°. Find the exact values of cos (–150°) and sin (–150°). Step 1:  Sketch an angle of –150° in standard position. Sketch a unit circle. x-coordinate = cos (–150°) y-coordinate = sin (–150°)

Homework: L13-1 (page 725) #1-15, 23-25 L13-2 #2-40e