sketch the graphs of the functions y = cos x , y = cos 2 x and y = cos 1 2 x for 0 ≤ x ≤ 360 ° . Check with your GDC or with dynamic geometry software.

Let's consider the trigonometric function y = cos x x 0 90 ° 180 ° 270 ° 360 ° y 1 0 - 1 0 1 Graph of y = cos x is Let's consider the trigonometric function y = cos 2 x x 0 45 ° 90 ° 135 ° 180 ° y 1 0 - 1 0 1 On the same axes graph of y = cos 2 x is Let's consider the trigonometric function y = cos 1 2 x x 0 90 ° 180 ° 270 ° 360 ° y 1 1 2 0 - 1 2 - 1 Graph of y = cos 1 2 x is

sketch the graphs of the functions y = cos x , y = cos 2 x and y = cos 1 2 x for 0 ≤ x ≤ 360 ° . Check with your GDC or with dynamic geometry software. Add the graph of y = 2 cos 2 x to your sketch.

Let's consider the trigonometric function y = cos x x 0 90 ° 180 ° 270 ° 360 ° y 1 0 - 1 0 1 Graph of y = cos x is Let's consider the trigonometric function y = cos 2 x x 0 45 ° 90 ° 135 ° 180 ° y 1 0 - 1 0 1 On the same axes graph of y = cos 2 x is Let's consider the trigonometric function y = cos 1 2 x x 0 90 ° 180 ° 270 ° 360 ° y 1 1 2 0 - 1 2 - 1 Graph of y = cos 1 2 x is Now, graph of y = 2 cos 2 x is

Predict how the graph of y = cos x changes when it is transformed to y = cos 1 2 x . Predict the period of the graph of y = cos 1 2 x . Check with your GDC or geometry software.

Let's consider the trigonometric function y = cos x x 0 90 ° 180 ° 270 ° 360 ° y 1 0 - 1 0 1 Graph of y = cos x is Let's consider the trigonometric function y = cos 1 2 x x 0 90 ° 180 ° 270 ° 360 ° y 1 1 2 0 - 1 2 - 1 Graph of y = cos 1 2 x is We know that, a graph of f x stretches horizontally by c when it is transformed to f 1 c x , c > 1 Period of cos x is 360 ° The period is the horizontal length of one complete cycle. Therefore, the period of the graph is 720 ° .

sketch the graphs of the functions y = cos x , y = cos 2 x and y = cos 1 2 x for 0 ≤ x ≤ 360 ° . Check with your GDC or with dynamic geometry software. Add the graph of y = 2 cos 2 x to your sketch. Write down the amplitude and period of each graph, in a table like this: Graph y = cos x y = cos 2 x y = 2 cos 2 x Period Predict how the graph of y = cos x changes when it is transformed to y = cos 1 2 x . Predict the period of the graph of y = cos 1 2 x . Check with your GDC or geometry software. Add a column for y = cos 1 2 x to your table.

Let's consider the trigonometric function y = cos x x 0 90 ° 180 ° 270 ° 360 ° y 1 0 - 1 0 1 Graph of y = cos x is Let's consider the trigonometric function y = cos 2 x x 0 45 ° 90 ° 135 ° 180 ° y 1 0 - 1 0 1 On the same axes graph of y = cos 2 x is Now, graph of y = 2 cos 2 x is The amplitude of a curve is half the distance between the maximum and minimum values. The period is the horizontal length of one complete cycle. From the graph, we can observe - 1 ≤ sin x ≤ 1 - 1 ≤ sin 2 x ≤ 1 - 2 ≤ 2 sin 2 x ≤ 2 Graph y = cos x y = cos 2 x y = 2 cos 2 x amplitude 1 1 2 Period 360 ° 180 ° 180 ° Let's consider the trigonometric function y = cos 1 2 x x 0 90 ° 180 ° 270 ° 360 ° y 1 1 2 0 - 1 2 - 1 Graph of y = cos 1 2 x is We know that, a graph of f x stretches horizontally by c when it is transformed to f 1 c x , c > 1 Period of cos x is 360 ° The period is the horizontal length of one complete cycle. Therefore, the period of the graph is 720 ° . Graph y = cos x y = cos 2 x y = 2 cos 2 x y = cos 1 2 x amplitude 1 1 2 1 Period 360 ° 180 ° 180 ° 720 °

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>How Do They Measure Up?>Chapter 8 - Trigonometric Functions>Exploration 3

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 7: Exploration 3

Author:Rose Harrison, Clara Huizink, Aidan Sproat Clements & Marlene Torres Skoumal

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 7: Exploration 3

Attempt the free practice questions from Exercise 7: Exploration 3 with hints and solutions to strengthen your understanding. Extended MYP Mathematics A Concept based approach Years 4 & 5 solutions are prepared by Experienced Embibe Experts.

Questions from Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 7: Exploration 3 with Hints & Solutions

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 1

Describe the effect on the graph of $y = f (x)$ when it is transformed to $y = f (2 x)$ .

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 7

sketch the graphs of the functions $y = \cos x, y = \cos 2 x$ and $y = \cos \frac{1}{2} x$ for $0 \leq x \leq 360 °$ . Check with your GDC or with dynamic geometry software.

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 7

sketch the graphs of the functions $y = \cos x, y = \cos 2 x$ and $y = \cos \frac{1}{2} x$ for $0 \leq x \leq 360 °$ . Check with your GDC or with dynamic geometry software.

Add the graph of $y = 2 \cos 2 x$ to your sketch.

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 7

sketch the graphs of the functions $y = \cos x, y = \cos 2 x$ and $y = \cos \frac{1}{2} x$ for $0 \leq x \leq 360 °$ . Check with your GDC or with dynamic geometry software.

Add the graph of $y = 2 \cos 2 x$ to your sketch.

Write down the amplitude and period of each graph, in a table like this:

$\begin{matrix} Graph & y = \cos x & y = \cos 2 x & y = 2 \cos 2 x \\ Period \end{matrix}$

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 7

Predict how the graph of $y = \cos x$ changes when it is transformed to $y = \cos \frac{1}{2} x$ . Predict the period of the graph of $y = \cos \frac{1}{2} x$ . Check with your GDC or geometry software.

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Exploration 3>Q 7

sketch the graphs of the functions $y = \cos x, y = \cos 2 x$ and $y = \cos \frac{1}{2} x$ for $0 \leq x \leq 360 °$ . Check with your GDC or with dynamic geometry software.

Add the graph of $y = 2 \cos 2 x$ to your sketch.

Write down the amplitude and period of each graph, in a table like this:

$\begin{matrix} Graph & y = \cos x & y = \cos 2 x & y = 2 \cos 2 x \\ Period \end{matrix}$

Predict how the graph of $y = \cos x$ changes when it is transformed to $y = \cos \frac{1}{2} x$ . Predict the period of the graph of $y = \cos \frac{1}{2} x$ . Check with your GDC or geometry software.