Describe how to transform the graph of y = sin x to y = - sin 1 3 x .

We are given to transform the graph of y = sin x to y = - sin 1 3 x . Translation: For the sinusoidal functions f ( x ) = sin x and f ( x ) = cos x , y = f ( x ) + d translates y = f ( x ) by d units in the y -direction. i) when d > 0 , the graph moves in the positive y -direction (up). ii) when d < 0 , the graph moves in the negative y -direction (down). Dilation: For the sinusoidal functions f ( x ) = a sin b x and f ( x ) = a cos b x : i) y = a f ( x ) is a vertical dilation of f x , scale factor a , parallel to the y -axis. a is the amplitude. ii) y = f ( b x ) is a horizontal dilation of f x , scale factor 1 b , parallel to the x -axis. b is the frequency. Now, to transfer y = sin x to y = sin 1 2 x + 3 , we need to do the following step:- i) Draw the graph for y = sin x . ii) Dilate the frequency horizontally along the x -axis by a scale factor 3 , as shown in the figure below. iii) Take the image of whole graph about x -axis. This is the required graph.

Describe how to transform the graph of y = cos x to y = - 3 cos x .

We are given to transform the graph of y = cos x to y = - 3 cos x . Translation: For the sinusoidal functions f ( x ) = sin x and f ( x ) = cos x , y = f ( x ) + d translates y = f ( x ) by d units in the y -direction. i) when d > 0 , the graph moves in the positive y -direction (up). ii) when d < 0 , the graph moves in the negative y -direction (down). Dilation: For the sinusoidal functions f ( x ) = a sin b x and f ( x ) = a cos b x : i) y = a f ( x ) is a vertical dilation of f x , scale factor a , parallel to the y -axis. a is the amplitude. ii) y = f ( b x ) is a horizontal dilation of f x , scale factor 1 b , parallel to the x -axis. b is the frequency. Hence, to transform the graph of y = cos x to y = - 3 cos x , we need to do the following step: i) Draw the graph for y = cos x . ii) Multiply the amplitude (value of y ) by 3 . iii) Then, reflect the graph of y = 3 cos x on x -axis to obtain the required graph of y = - 3 cos x as shown below.

Draw the graph of the function y = 5 2 sin - x 3 showing at least two cycles. Be sure to clearly indicate the amplitude and period.

Given function is y = 5 2 sin - x 3 We know that the amplitude is the height from the mean value of the function to its maximum or minimum value. Thus, the amplitude of the given function = 5 2 Period of the function = 360 ° 1 3 = 1080 ° Thus, the graph of the given function is as follows:

HARD

MYP:4-5

IMPORTANT

Earn 100

Describe how to transform the graph of $y = \sin x$ to $y = 0.5 \sin x + 4$ .

Important Questions on Trigonometric Functions

HARD

MYP:4-5

IMPORTANT

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

Describe how to transform the graph of

y = \sin x

y = - \sin (\frac{1}{3} x)

HARD

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Practice 5>Q 2

Describe how to transform the graph of

y = \cos x

y = - 3 \cos x

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Practice 6>Q 1

After you exercise, the velocity of air flow(in $litres$ per $second$ ) into your lungs can be modelled by the equation $y = 2 \sin (90 ° t)$ .

Draw the graph of the function in the first $8 seconds$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Practice 6>Q 5

When you ride a Ferris wheel, your vertical height above the ground changes. The relationship between your height above the ground and the time for a complete revolution of the wheel can be modelled with the sinusoidal graph given below. Find a function that models the graph.

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EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Practice 6>Q 6

The height in meters of the tide above the mean sea level on one day at Bal Harbour can be modelled by the function $h (t) = 3 \sin 30 ° t$ , where $t$ is the number of hours after midnight. A ship can cross the harbour if the tide is at least $2 m$ above the average sea level. Determine the time when it can cross the harbour.

MEDIUM

MYP:4-5

IMPORTANT

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

For the following graph, find the amplitude, frequency, and period. Then, write down the equation that represents the function.

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MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Mixed practice>Q 2

Draw the graph of the function

y = \frac{5}{2} \sin (\frac{- x}{3})

showing at least two cycles. Be sure to clearly indicate the amplitude and period.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 8 - Trigonometric Functions>Mixed practice>Q 9

A Ferris wheel has a radius of $10$ meters. The bottom of the wheel is $2$ meters above the ground. The wheel, rotating at a constant speed, takes $100$ seconds to complete one revolution. Draw a graph of your function.

Describe how to transform the graph of y=sinx to y=0.5sinx+4.

Important Questions on Trigonometric Functions

Learn and Prepare for any exam you want !

Describe how to transform the graph of $y = \sin x$ to $y = 0.5 \sin x + 4$ .