Aim: How do we graph and Do Now: Fill in the table for the equation : x y HW: p.440 # 1 – 6, p.446 # 3 – 6

y = sin x

y = sin x is the basic sine curve and there are some transformations based on it that will be discussed later. The sine curve keeps going forever on both directions, there is a complete curve every 2π radians (360  ), that is the curve repeat itself every 2π radians. This is called period function The value of y is within 1 and –1. We say the function has amplitude is 1. Period: within which lies one complete curve Amplitude: Range of the function. Always + or – 1

We look at the curve in 4 quadrants In the first (0 to π), the curve increase from 0 to 1 In the second (π/2 toπ), the curve decreases from 1 to 0 In the third (πto ), the curve continues to decrease from 0 to –1 In the fourth ( to ), the curve increases again from –1 to 0

To graph y = cos x, we use the same method x y y = cos x

The basic cosine curve has a period of just like the sine curve but here the maximum and minimum points are different. For the sine curve the maximum points are at etc – every etc.,while the minimum points are For the cosine curve the maximum points are at etc. also every while the minimum points are at etc.

The x - intercept and y – intercept of both sine and cosine curve For the sine curve they are at 0, the wholes. For the cosine curve they are at halves,, etc. Most important for graphing is recognizing the y-intercept. The y-intercept for sine curve is 0 as the curve passes through the origin while for the cosine curve the y-intercept is 1.