Maths edexcel set b silver chapter 7

9

https://imgur.com/a/3hD5lIB

Could someone help me with c ii? I got the equation into 5cos2x -4sin2x +5 and know the maximum of both cos and sin is 1 but I don’t know how to get the answer.

Reply 1

mqb2766

21

Original post

by saminasb3

https://imgur.com/a/3hD5lIB
Could someone help me with c ii? I got the equation into 5cos2x -4sin2x +5 and know the maximum of both cos and sin is 1 but I don’t know how to get the answer.

Assuming youre right about ci), you should have covered the harmonic identity or how to convert
a*cos(x) + b*sin(x)
into c*cos(x + alpha) say and how c is related to a and b? Its simply circles/pythagoras if you want to think about it like that.

Reply 2

Nitrotoluene

11

Original post

by saminasb3

https://imgur.com/a/3hD5lIB
Could someone help me with c ii? I got the equation into 5cos2x -4sin2x +5 and know the maximum of both cos and sin is 1 but I don’t know how to get the answer.

Hello saminasb3!

Trig solution
==>Simplify using the trigonometric identity: cos^2(x) + sin^2(x) = 1
==>Rewrite the function using the trick above.
==>Use the fact that sin(x) and cos(x) are both bounded by -1 and 1 to find the maximum.
==>Now I think you can continue on your own.

*°*°*°*

I don't know your current maths syllabus. Now, I am suggesting an additional method.
If you are studying or have studied "Calculus", you can solve the problem by working as follows:
==>Find the first derivative
after
==>Find the critical points (very complex, but you can use trigonometric identities to simplify the development)
after
==>Find the second derivative
after
==>Apply the second derivative test (very complex)
after
==>Evaluate the function at critical points
==>End of distress.
Ciao,
The flag of Italy.png

Sandro

My signature: "Regardless of where you may be, expressing gratitude is a universally cherished gesture."

(edited 10 months ago)

Reply 3

username79352

OP

9

Original post

by mqb2766

Assuming youre right about ci), you should have covered the harmonic identity or how to convert
a*cos(x) + b*sin(x)
into c*cos(x + alpha) say and how c is related to a and b? Its simply circles/pythagoras if you want to think about it like that.

Yes I didn’t manage to see that straight away. I got 5+ square root 41

Reply 4

mqb2766

21

Original post

by saminasb3

Yes I didn’t manage to see that straight away. I got 5+ square root 41

Sounds about right. Its just pythagoras on the sin/cos coeffs, which is equivalent to the radius of the circle.

Reply 5

davros

16

Original post

by Nitrotoluene

Hello saminasb3!
Trig solution
==>Simplify using the trigonometric identity: cos^2(x) + sin^2(x) = 1
==>Rewrite the function using the trick above.
==>Use the fact that sin(x) and cos(x) are both bounded by -1 and 1 to find the maximum.
==>Now I think you can continue on your own.

*°*°*°*

I don't know your current maths syllabus. Now, I am suggesting an additional method.
If you are studying or have studied "Calculus", you can solve the problem by working as follows:
==>Find the first derivative
after
==>Find the critical points (very complex, but you can use trigonometric identities to simplify the development)
after
==>Find the second derivative
after
==>Apply the second derivative test (very complex)
after
==>Evaluate the function at critical points
==>End of distress.
Ciao,
The flag of Italy.png

Sandro

My signature: "Regardless of where you may be, expressing gratitude is a universally cherished gesture."

Have you posted this from chatgpt or somewhere, because it's completely unhelpful for the question as posted!

Part c)(i) specifically asks for the function to be written in terms of double angles (2x) and part c)(ii) specifically starts with the word "hence", which indicates that the required answer must come from the result of part c)(i).

Your method might be technically valid for a different question, but it would get no marks here!

Maths edexcel set b silver chapter 7

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