Aim; How do we graph trig functions?

Aim; How to do we graph trigonometric functions?

In order to graph trigonometric function you need to 1) beable to determine if a function is sin or cos , you also need to be able to determine 2) The amplitude, period and midline of a function .

A sin trig function views as;

A cos trig function views as;

The formula for a trigonometric function is y=Acos(Bx) or  y=Asin(Bx)


- Now you need to find the amplitude, in order to find the amplitude of the you need to locate the maximum value and the minimum value and subtract them, you then divide that number by 2. Your result serves as your amplitude or your "A" in the function.

- To locate the period of the function or your(Bx) youll be using 2(pi) over the cycle number, which if you look above  to the example are the numbers on the x -axis.

- in order to determine the midline locate the max and the minimum again and then add or you can visually determine the line that is in the middle of the function horizonally. This number will serve as the number you add or subtract in your function For example; y=Acos(bx) + 6. The six wouldve been the midline of a function.







Work cite for images only:
The biology project ,april 2006, http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphtrigfunctions.html

Properties of trigonometri fucntions,http://www.analyzemath.com/trigonometry/properties.html

2/25/13 How do we convert between radians and degrees?

How do we convert between Radians and Degrees ?

Reference angle - the smallest angle that the terminal side if the given angle makes with the x- axis

Radians - one radian is the angle subtended at the center of a circle by an arc that is equal length to the radius of the circle
1 radian = 180/pi = 57.2958

-To convert from Radians to degrees;
Example : 2(pi) x 180 / pi
The (pi) cancel each other out and you're left with (2x180) with equals 360 degrees
Example 2 : 5(pi) x 180/12(pi)
The pi cancel each other out then your left (5x180) = 900/12 then your final answer is 75 degrees


To convert from degrees to radians;
 *Always leave in terms of pi when converting to radians

Example :
60/180(pi) = 1/3(pi) reduce ----> (pi)/3
 Example 2 :
45/180(pi) = 11/12(pi) this can not be reduced








Bibliography (images only)
regentsprep.org ,http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm
Radians , mathisfun.com , http://www.mathsisfun.com/geometry/radians.html

1/7/13 how do we solve exponential equations ?

How do we solve exponential equations ?

 How to solve 100 +10 ^x where the 'x' is unknown but you that 10 *10 is 100 so "x' equals 2
When the bases/ numbers are the same the exponents must be equal as well
solve for 3^x+4 = 3^7
first just set up the exponents like an equation : x+4 = 7 , the solve algebraically
x will equal =11
11 is the new exponent

 Try this with ; 2 ^3x+7 = 2^5x-1
  set up the exponents 3x+7 =5x-1 then solve algebraically
then end result will be that x= 4 this becomes the new exponent

1/713 how do we solve complex fractions?

How do we solve complex fractions?

When you see a complex fraction , it usual consists of another fraction for example;
1/1/3
The first step its rewrite it as 1 divided by 1/3

Then you do the reciprocal to the "1/3" so you can turn the divisor bar into multiplication so it become 3/1 or 3
Then it becomes1*3 and the end result is 3

Try with another example :
1/1/x+1
so first write it as 1 divided by 1/x+1
then do the reciprocal to change the sign so it becomes multiplication ; 1* x+1
now multiply and your result becomes x+1

12/18/12 How do we add and subtract rational expression ?

How do we add and subtract rational expressions ?

-When adding and subtracting rational expressions, it takes the same method as adding and subtracting fractions.
Example : 4/x+8 +3/x-8
First find a common denominator of the expression ;
4/(x+8)(x-8) + 3 (x-8)(x+8)
Now whatever you multiplied on the bottom to find the common denominator , you must multiply to the numerator:
4(x-8)+3(x+8)
Now solve and simplfy:
4x-32+3x+24 =7x-8
Put this over your denominator :
7x-8/(x+8)(x-8) or 7x-8/x^2-64
Either of the above would be a valid  answer






work citations ;
Regents exam questions , Algebra 2& trigonometry practice: addition and subtraction of rationals, pg 3, www.jmap.org

1/2/13; How do we add and subtract rational expressions?

How do we add and subtract rational expressions?

Adding and subtracting rational expressionals are much like cross multiplying or adding and subtracting fractions , for example ;

First find the common denominator : 1/x + x/2y
the common denominator would be :2xy

 Next, after finding the common denominators remember that whatever you multiply to the bottom you multiply to the top as well : 2y/2xy +x^2 /2xy

Now combine the expression : 2y +x^2 /2xy and that would be your final result

12/4/12 how do we rationalize a denominator?

How do we rationalize a denominator?

There are two different ways you can rationalize a denominator , first understand that you can never have a radical as a square root for example : 5 over radical 9

- in order to solve this you would have to simplify the bottom by finding the square root so this becomes 5/3

Then you might come to more complex problems like 5/3+(rad.)2
the way you would solve this problem is by using the complex conjugate of the denominator so you would have (3+(rad)2)(3-(rad)2) then FOIL this
the foiled product would be ; 9-3(rad)2+3(rad)2-(rad)4 , next you need to combine like terms and the final product 11
Now you need to multiple the same number on the bottom to the top so it would be (5)(3-(rad.)2)
 this results to 15-5(rad)2/11 as the final product