Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle Common Core Standards for Chapter 6 The arc in this example is notated by s. The angle is notated by The radian measure of this angle is s. If this angle is, the radian measure would be:

Chapter 6 Sec 1: Angles and Radian Measure To change degrees to radians, just multiply by = 120* Ex: change 120to radian measure in terms of ***radian measures are not given in decimals!!! To change radians to degrees, multiply by Ex: changeradians to degree measure. =315

The arc length of a circle is equal to the product of the radius and the radian measure of the central angle it sub tends. S=r Ex: Given a central angle of 125 degrees, find the arc length of its intercepted arc in a circle of radius 7centimeters. Round to the nearest tenth. 1. Change the degrees to radians. 2.Multiply the radians measurement by the radius of the circle The arc length of this angle is 15.3 cm.

Ex: The Swiss have long been highly regarded as makers of fine watches. The central angle formed by the hands of the watch on "12" and "5" is 150 degrees. The radius of the minute hand is (3/4) cm. Find the distance traversed by the end of the minute hand from "12" to "5" to the nearest hundredth of a centimeter. To evaluate the trig of a radian: Ex: Evaluate is 240 in degree mode, so we're just finding the cos of 240. Using my calculator, I find cos 240 is -1/2. Assignment: page : 5-12, STOP!!!

Chapter 6 Sec 3 &4: Graphing Sine and Cosine Functions The period of a function is the interval along its graph where the same values repeat. The period for the sine function and cosine function is Period Starts at 0 Goes up to 1 Comes back to 0 Goes down to -1 Comes back to 0 From - to 0 is a period of this function. After 0, it repeats.

A better look:

What you need to know about the graph of y=sinx: 1. The period of the function is 2. The domain of the function is all real numbers, and the range is all real numbers between -1 and The x intercepts are located at where n is an integer. What you need to know about the graph of y=cosx: 1. The period of the function is 2. The domain of the function is all real numbers, and the range is all real numbers between -1 and The x intercepts are located at where n is an integer.

Period

The amplitude of the functions of y=Asin and y=Acos is the absolute value of A. The period of the functions y=sink and y=coskis Ex: state the period for the function y=cos Rewrite the function asso k= Then the amplitude is

Ex: graph y=cosand y=cos Y= cos(x)

Y=cos1/4x with same x,y axis lengths. Can you see the differences in these graphs??

Ex: state the amplitude and the period for the function y=5 cos 2 Ex: Write an equation of the sine function with amplitude 2 and period Answer: amplitude:5, period: pi Answer:y=2sin4x

Use your calculator. Just make sure it is in radian mode. Finding trig for radian measures: Ex: find is 1. Find the value for which=0 is true. Since we're finding where it equals 0, we are also looking for where it crosses the x axis. According to the properties of the sin function (slide 7 and in your book page 360), it crosses the x axis at every interval of.

Find the value of for which is true. Look at the graph of sin: Where the graph is -1. These are all multiples of You have to determine how big a multiple. Find the distance between each arrow. In this case it's ? So the answer is where n is an integer. Stop!!! Assignment page , 31,32 Page , 17-22, 23-26, even

Chapter 6: Sec 5: Translations of Sine and Cosine Functions A horizontal shift or translation of a trig function is called a phase shift. The phase shift of a function and is, where k >0. If c>0, the shift is to the left. If c<0, the shift is to the right. The frequency of a trig function is the number of cycles it completes in a given interval. Usually the interval is The midline is the new horizontal axis created by a vertical shift.

Ex: When a constant is added to a sine or cos function, the graph is is shifted upward or downward. If (x,y) are the coordinates of y=sinx, then (x, y+d) are the coordinates of y=sinx+d Graph:

The vertical shift of the functions and is h. If h>0, the shift is upward. If h<0, the shift is downward. The midline is y=h. The midline is a new horizontal axis. State the vertical shift and the equation of the midline for the function: To graph sine and cosine functions: 1. Determine the vertical shift and graph the midline. 2.Determine the amplitude. Use dash lines to record the max and min values. 3.Determine the period of the function. 4.Determine the phase shift and translate the graph.

Ex: State the amplitude, period, phase shift, and vertical shift for each, then graph

Steps for graphing using last example:

STOP!!! Do worksheet on ch 6 sec 5!!! Then do pages in your book. #'s:15, 17, 22, 24, 26, Quiz Thursday on Everything so far in Chapter 6!!!!!!!!!