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Trigonometric Functions help

Hi

I'm trying to learn trigonometric functions,

The question is to:

express 4.sin(Ωt+1.2°) in the form of a.sin(Ωt) ± b.cos(Ωt)

I wanna use an argand diagram to verify my answer


Thanks!
What is the question?
Reply 2
Avatar for dc2209
dc2209
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Original post by poorform
What is the question?


express 4.sin(Ωt+1.2°) in the form of a.sin(Ωt) ± b.cos(Ωt)
Reply 3
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dc2209
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Original post by dc2209
express 4.sin(Ωt+1.2°) in the form of a.sin(Ωt) ± b.cos(Ωt)


using compound angle formula
Reply 4
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razzor
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Are you familiar with the addition formulae for trigonometric functions?
Reply 5
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dc2209
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Original post by razzor
Are you familiar with the addition formulae for trigonometric functions?


nope
Reply 6
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razzor
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These might help you out:

sin(A+B) = sin(A)cos(B) + sin(B)cos(A)
sin(A-B) = sin(A)cos(B) - sin(B)cos(A)

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
Reply 7
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dc2209
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Original post by razzor
These might help you out:

sin(A+B) = sin(A)cos(B) + sin(B)cos(A)
sin(A-B) = sin(A)cos(B) - sin(B)cos(A)

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
cos(A-B) = cos(A)cos(B) + sin(A)sin(B)


yes that is the compound angle formula i mentioned
Reply 8
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razzor
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So substitute the appropriate values into the formula for sin(A+B) and see what you get. Compare it with a.sin(Ωt) ± b.cos(Ωt).
Reply 9
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dc2209
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Original post by razzor
So substitute the appropriate values into the formula for sin(A+B) and see what you get. Compare it with a.sin(Ωt) ± b.cos(Ωt).


Ok so 4[sin+Ωt] x cos1.2 + cosΩt x sin 1.2]
Reply 10
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razzor
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Original post by dc2209
Ok so 4[sin+Ωt] x cos1.2 + cosΩt x sin 1.2]


"sin+Ωt" doesn't mean anything. You can't have sine plus an angle.
Also, I don't why you put another squared bracket after the Ωt. The 4 needs to multiply the whole thing.
Reply 11
Avatar for van.domo
van.domo
Original post by dc2209
Hi

I'm trying to learn trigonometric functions,

The question is to:

express 4.sin(Ωt+1.2°) in the form of a.sin(Ωt) ± b.cos(Ωt)

Hello. I have attahced a solution below. If you obtain a copy of the Edexcel A Level Mathematics core 3 syllabus, it explains how to undertake Trig questions like yours, using compound angle formulae. It is a compound angle as A is not the same as B. If A was the same as B, then it would be Double Angle Formulae.

As for an Argand Diagram, these are used in conjunction with Complex Numbers, which are part of the Edexcel Further Pure 1 syllabus.

For further help and support on Trig Identities, please visit Exam Solutions.net or www.m4ths.com.

Thanks
Vandomo
Student Room Trig Identity Question.jpg136.1KB
Reply 12
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dc2209
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[QUOTE="van.domo;57379937"]
Original post by dc2209
Hi

I'm trying to learn trigonometric functions,

The question is to:

express 4.sin(Ωt+1.2°) in the form of a.sin(Ωt) ± b.cos(Ωt)

Hello. I have attahced a solution below. If you obtain a copy of the Edexcel A Level Mathematics core 3 syllabus, it explains how to undertake Trig questions like yours, using compound angle formulae. It is a compound angle as A is not the same as B. If A was the same as B, then it would be Double Angle Formulae.

As for an Argand Diagram, these are used in conjunction with Complex Numbers, which are part of the Edexcel Further Pure 1 syllabus.

For further help and support on Trig Identities, please visit Exam Solutions.net or www.m4ths.com.

Thanks
Vandomo



Ah thanks, that makes sense.

in my notes I have d = tan^(-1) 0.083/3.996 = (this should be 2 degrees), is this for construction of the argand diagram?

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