Search Header Logo

Harmonic form & trig modelling

Authored by James Attwood

Mathematics

11th - 12th Grade

Used 4+ times

Harmonic form & trig modelling
AI

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

    Content View

    Student View

7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Given that

 2sin x5cos x3cos (x+a)2\sin\ x-\sqrt{5}\cos\ x\equiv-3\cos\ \left(x+a\right)  .
Find the value of  aa  in degrees.

48.1

41.8

33.7

36.7

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 cos(x) 3sin(x)Rcos(x+a)\cos\left(x\right)\ -\sqrt{3}\sin\left(x\right)\equiv R\cos\left(x+a\right)  .
Given that  R>0R>0 , find  RR   . 

 10\sqrt{10}  

 2\sqrt{2}  

 3\sqrt{3}  

 22  

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt


Part 1:
 f(x)=sin(x)+3cos(x).f\left(x\right)=\sin\left(x\right)+3\cos\left(x\right).  


By writing  f(x)=Rsin(x+a)f\left(x\right)=R\sin\left(x+a\right)  , find the maximum value of  f(x)f\left(x\right)  .

10

4

 10\sqrt{10}  

3

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Part 2:
 f(x)=sin(x)+3cos(x)f\left(x\right)=\sin\left(x\right)+3\cos\left(x\right)  

Using your workings from the last question, find the only value of  0a90°0\le a\le90\degree  where this maximum value occurs.


69.2

0

71.6

18.4

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Media Image

0.1m

0.1cm

0.7m

1.4m

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Media Image

80

105

130

70

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Media Image

(t is in radians)

March

April

May

June

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?