• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15

# trigonometric functions

Extracts from this document...

Introduction

Portfolio

Type 1 investigation

Transformation of Trigonometric Functions

Investigate the function:

y = a sin b(x-c) + d   in respect to the transformation of the base curve of y = sin x, depending on the values of a, b, c, and d. Be sure to consider all possible values for a, b, c, and d.

Describe the base curve

Then try values in b (sin2x, sin -3x, sin1/2x)

Does your hypothesis hold true for y = cos(x) and y = a cos b (x-c) +d? How about tan(x)?

Transformation of Trigonometric Functions

Introduction

The purpose of this study is to examine the transformation of trigonometric functions of y=A sin B (x-C) + D and determine the effect on the base curve y=sin(x). I am going to be systematically changing the values of A, B, C and D in the equation y= A sin B (x-C) +D. First I am going to examine different numbers for the value of A. I am going to use whole numbers, negative whole numbers, positive rational numbers and negative rational numbers for the value of A and see how this affects the Sine curve. Then I will examine different numbers for B, then C then D.

Middle

Figure 9                                                Figure 10

These graphs show that my prediction was correct, as figure 9 shows that the minimum value is -0.4 and figure 10 shows that the maximum value is 0.4, and both figures show that the period is 2 π.

Changing the value of constant B

I am now going to change the values of B in the equation y= sin(Bx) to see what affect it has on the base curve.

Y=sin (3x)

Figure 11

Figure 11 shows that the amplitude, maximum and minimum values have the same value as the curve y=sinx, i.e  1 and -1. The period of y=sin3(x) has decreased from 2 π to π/3. It is also noticed that increasing the value of ‘B’ to 3, the curve repeats itself three times within the period f 2 π. So this shows that large values for ‘B’ have a smaller period but a larger frequency. So this shows that ‘B’ affects the period which affects the frequency of the equation.

Y=sin (-3x)

Figure 12

Figure 12 shows that the amplitude and maximum value remain 1 while the minimum value remains -1. And that the period also decreased from 2 π to π /3. Once again using the trace option on the graphing calculator, we notice that using a negative value inverts the curve.

Y= sin (0.25x)

Figure 13                                                Figure 14

Conclusion

Y=sin (x)+ 2/5

Figure 26

Figure 26 shows my prediction is correct.

After examining what happens when changing all values in the equation, y= A sin B (x-C) +D, I am now going to predict what changes will occur is I used the equation y= 5 sin -2 (x-1) + ¾. I predict that the maximum value will change to 5, the minimum value will change to -5 and the amplitude will change to 5. The base curve is inverted because the ‘B’ value is a negative value and the period of the curve is decreased to π which increases the frequency to 2. The base curve also shifts to right by 1 unit and shifts vertically upwards by 0.75 (changing the maximum value to 5.75 and the minimum value to -4.25).

Figure 27

Figure 28                                                        Figure 29

Figure 27 above shows that my prediction is correct. Figure 28 proves shows that my prediction about the maximum value being 5.75 is correct. And Figure 29 using the trace button shows that my prediction about the curve having a phase shift to the right by one unit.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## LACSAP's Functions

- 0(7 - 0) = 28 1 28 ( (7+1)C2) - 1(7 - 1) = 22 2 28 ( (7+1)C2) - 2(7 - 2) = 18 3 28 ( (7+1)C2) - 3(7 - 3) = 16 4 28 ( (7+1)C2) - 4(7 - 4) = 16 5 28 ( (7+1)C2)

2. ## Analysis of Functions. The factors of decreasing and decreasing intervals (in the y ...

and the range are not all the values of y, the range are only the values larger than zero to positive infinite. There is not periodicity in any of these functions because in a function f(x+a)=f(x), a is not constant so there is not periodicity.

1. ## Population trends. The aim of this investigation is to find out more about different ...

In most cases the points are very close to the graphed line. The model shows how the population increased correctly although it should be more curved order to be able to represent what actually happened. The model shows a reasonable past where population was less than in 1950.

2. ## Mathematics Higher Level Internal Assessment Investigating the Sin Curve

The first thing that we found out was that the variable represents the amplitude of the graph meaning the height of the graph. The amplitude of the graph would be the value of . On the other hand, the value of corresponds to the period of the curve where the period is given by .

1. ## Function Transformation Investigation

* So for the moment, adding or subtracting a number to a function's output or input has translated it horizontally by adding or subtracting to the input, and vertically by adding or subtracting to the output. The translation compared to the original function can be predicted by this method: Will be a horizontal translation, right, by -a.

2. ## Shady Areas. In this investigation you will attempt to find a rule to approximate ...

For each diagram, find the approximation for the area. What do you notice? Various diagrams will be created to depict the increasing number of trapeziums, which result in a greater precision for the approximation for the area. Number of Trapeziums Manual Calculations Riemann Sum Application Graphs (Y = x2 + 3)

1. ## Approximations of areas The following graph is a curve, the area of this ...

A(1) .376 A (3) .388 Trapezium (4) Trapezium (5) Trapezium (6) .435 Trapezium (7) Trapezium (8) A(8) A A(1) + A(2) + A(3) + A(4) + A(5) + A(6) + A(7) + A(8) A .376 + .380 + .388 + .399 + .415 + .435 + .458 + .485 A 3.336 The approximated area of the graph under the

2. ## The investigation given asks for the attempt in finding a rule which allows us ...

last base and n = number of trapeziums. Taking an example from the previous question, the general statement is basically a compacted form of the area formulas for n trapeziums hence: A=12hfa+fx1+12hfx1+fx2+?+12hfxn-1+gb However, further simplifying the equation, and taking into account that first and lase base are only used twice the entire time, the expression would appear as

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to