Write down the amplitude, frequency and period of the function y = 4 cos 3 x , for 0 ° ≤ x ≤ 360 ° then sketch the graph for the domain. Check your graphs on a GDC or graphing software.

Given that, y = 4 cos 3 x , for 0 ° ≤ x ≤ 360 ° Amplitude = a = 4 Frequency = f = 3 Period = 360 f = 360 4 = 120 at x = 0 , y = 4 × cos 3 × 0 = 0 , at x = 30 , y = 4 cos 120 = 0 , at x = 60 , y = 4 cos 180 = - 4 , at x = 90 , y = 4 cos 270 = 0 and at x = 120 , y = 4 cos 360 = 4 . x 0 30 60 90 120 y 4 0 - 4 0 4 The graph can be drawn with the help of given point as follows,

Draw the graph of the function y = - sin x for 0 ° < x ≤ 360 ° . Be sure to clearly indicate on your graph the amplitude, the y - intercept and the period.

Given that, the trigonometric function is y = sin x x 0 ° 90 ° 180 ° 270 ° 360 ° y 0 1 0 - 1 0 Hence, the graph is sketched and its x - coordinates are labelled. y = - f x = - sin x , Take the inverse image of graph of sin x about X-axis, To get the requires curve.

Describe how to transform the graph of y = cos x to y = cos 1 2 x + 2 .

To transform the graph of y = cos x to y = cos 1 2 x + 2 We need to do the following step:- 1) Draw the graph for y = cos x . Dilation: For the sinusoidal functions f ( x ) = a sin b x and f ( x ) = a cos b x , y = a f ( x ) is a vertical dilation of f ( x ) , scale factor a , parallel to the y - a x i s . a is the amplitude. y = f ( b x ) is a horizontal dilation of f ( x ) , scale factor 1 h , parallel to the x - a x i s . b is the frequency. Verify that y = a sin b x and y = - a sin b x have the same amplitude and period. 2) Shift the graph by 2 unit downward to get the required graph of equation y = cos 1 2 x + 2 from transformation rule of transforming f ( x ) to f ( x ) + d In this case you need to half the angle x and shift the given graph by 2 unit upward

EASY

MYP:4-5

IMPORTANT

Earn 100

Write the equation for the following graph.

Important Questions on Like Gentle Ocean Waves (Sine and Cosine Functions)

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 1>Q 1

Sketch the graph of the function $y = 4 \sin x$ . Label all the $x -$ intercepts on your sketch graphs.

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 3>Q 1

Write down the amplitude, frequency and period of the function

y = 4 \cos 3 x, for 0 ° \leq x \leq 360 °

then sketch the graph for the domain. Check your graphs on a GDC or graphing software.

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 4>Q 3

Draw the graph of the function

y = - \sin x

for

0 ° < x \leq 360 °

. Be sure to clearly indicate on your graph the amplitude, the

y -

intercept and the period.

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 5>Q 2

Describe how to transform the graph of

y = \cos x

y = \cos (\frac{1}{2} x) + 2

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 5>Q 3

The given graph is a transformation of either $y = \sin x$ or $y = \cos x$ . Identify the transformation on the graph and write the function that describes the graph.

Question Image

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 6>Q 1

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

Find the velocity (in lit/sec) of air flow at $4 s$ .

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Practice 6>Q 4

The height in meters (from its position at rest) of a spring as it bounces up and down can be modelled by the function $h (t) = 2 \sin (60 ° t) + 1$ , where $t$ is measured in seconds.

Determine if the amplitude is the same as the maximum height from its position at rest.

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 31 - Like Gentle Ocean Waves (Sine and Cosine Functions)>Mixed practice>Q 9

A Ferris wheel has a radius of $5$ meters and is $1$ meter above the ground. It takes $2$ minutes to make one complete revolution.

Find a function that models this Ferris wheel.

Write the equation for the following graph.

Important Questions on Like Gentle Ocean Waves (Sine and Cosine Functions)

Learn and Prepare for any exam you want !