Trigonometric

Functions Sine Definitions: 1. Amplitude: represents half the distance

between the maximum and minimum values

of the function and its given by: amplitude= |a|

2. Period: is the length of one cycle.

3. Phase Shift: When a period and graph are shifted by an amount.

4. Vertical Shift: A shift up or down.

5. Domain: all the x values.

6. Range: all the y values. Cosine: F(x)= Cos(2x-180)-3 1. To find the period I took 2pi and divided that by whats in front of the x (2)

2pi/2=180

2. To get the period interval I took the period and divided that by 4.

180/4=45

3. Then I took what is in the parenthesis and set it equal to 0 and 360.

2x-180=0 2x-180=360

2x=180 2x=540

x=90 x=270

4. 90 is my first x value that I used to find y and 270 was the last x value that i used to find y. You need 5 points to graph so to find the other 3 x values I added my period interval to 90 and so in and so forth until I get to 270.

5. To get the y values I plugged in each x into the equation.

(90, -2) (135, -3) (180, -4) (225, -3) (270, -2)

6. Then i graphed: Tangent 3sin(6x+pi)-2 1. Find your period.

period=2pi/b so period= 2pi/6

simplify: pi/3

2. Find your period-interval.

period-int= period/4 so period-int= pi/12

3. set what ever is in parenthesis equal to 0 and 2pi

6x+pi=0 and 6x=2pi

final results: x= -pi/6 and x= pi/6

your answer that was equal to zero is your starting point and 2pi is your ending.

4. To find x values, you add your period interval and to find your y values, substitute the x values and use your unit circle.

(-pi/6,0)(-pi/12,1)(0,0)(pi/12,-1)(pi/6,0)

5. Graph: Cosecant Secant F(x)=Sec(x-pi/2) 1. First to find period i took 2pi and divided that by whats in front of the x.

=2pi

2. To find the period interval i took 2pi and divided that by 4.

2pi/4= pi/2

3. Then i too what was in the parenthesis and set it equal to 2pi and 0

x-pi/2= 2pi x-2pi=0

x= 5pi/2 x=pi/2

4. I use those values as my x values. To find the remaining three values i add my period to pi/2.

5. To get my y values i plug my x values into the equation

= (pi/2,1) (pi,0) (3pi/2, -1) (2pi,0)

(5pi/2,1)

6. Then i graphed: 1. The first thing is to find the period using:

per.=2pi/b, so period=2pi/2 or pi

2. Find the period-interval:

period-interval = period/4, so pi/4

3. Set whatever is in parenthesis equal to 0 and 2pi and solve:

2x=0 and 2x=2pi

final results: x=0 and x=pi

remember that your answer for 0 is your starting point and your answer for

2pi in your ending

4. Add your period-int. to get the rest of your x values and to get your y values you

substitute in the x values and use the unit circle.

(0,-2)(pi/4,-1)(pi/2,-2)(3pi/4,-3)(pi,-2)

5. Graph: csc(2x)-2 cotangent Real World: One real world situation would be a roller coaster which is similar to both sine and cosine graphs. Another example could be the ocean with its up and down movements like the sine,cosine, and tangent graphs. Next, when using radar, cosecant is used to determine the radar and waves. Finally, you can use trig functions to monitor and model climates, this is used by meteorologists. f(x)=3tan(x)+2

1. To find the period, take pi over whatever number is in front of your x.

Period=pi

2. Since we do not use period-int for tan, you have take whatever is in parenthesis and set it equal to -pi/2 and +pi/2.

-pi/2=x

pi/2=x

3. Find you midpoint between your VA.

4. After, you have to do an x and y chart. Your x value is a number between your midpoint and Va.

pi/4 & -

For your y value you put your x number into your function and whatever you get is your y value.

5.Finally graph f(x)=4cot(x-180)

1.First, you must find your period. Since period for cot is pi, in degrees it would be 180(refer to unit circle).

2.Since we do not have a period-int, we need to find our VA. To find them you need to set your period equal to 0 and 180.

x-180=0 x-180=180

x=180 x=360

3. On your graph make a dotted line where your answers would be; in this case they would be x=180 and x=360.

4.Next, you must make an x and y chart.In order to do that you need to find your midpoints between 180 and 360 which happen to be 225 and 315. Put those numbers into your function for x and whatever you get is your y.

y=4 y=-4

5. Finally graph !

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# Trig.Done.Easy.

Step by step explanations to graphing Trigonometric Functions.

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