# Compound angles and Double angles?

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I don't understand any of the compound angle formulas and how to use them. I need help on this question:

sin(x+60)+cos(x+30)=0.5 between 0<x<360

Please help I'm struggling so bad.

sin(x+60)+cos(x+30)=0.5 between 0<x<360

Please help I'm struggling so bad.

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#2

They simply tell you how to rewrite sines and cosines of a number in a way that might be more useful.

You've probably seen the identities and

If you use that to rewrite sin(x+60) and cos(x+30) in those forms then it might be more obvious what to do next. In this case for the sine part you could have A as x and B as 60, and then for the cosine, A would be x and B would be 30.

You've probably seen the identities and

If you use that to rewrite sin(x+60) and cos(x+30) in those forms then it might be more obvious what to do next. In this case for the sine part you could have A as x and B as 60, and then for the cosine, A would be x and B would be 30.

Last edited by Sinnoh; 1 week ago

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(Original post by

They simply tell you how to rewrite sines and cosines of a number in a way that might be more useful.

You've probably seen the identities and

If you use that to rewrite sin(x+60) and cos(x+30) in those forms then it might be more obvious what to do next. In this case for the sine part you could have A as x and B as 60, and then for the cosine, A would be x and B would be 30.

**Sinnoh**)They simply tell you how to rewrite sines and cosines of a number in a way that might be more useful.

You've probably seen the identities and

If you use that to rewrite sin(x+60) and cos(x+30) in those forms then it might be more obvious what to do next. In this case for the sine part you could have A as x and B as 60, and then for the cosine, A would be x and B would be 30.

I don't understand what to do next.

Is it possible for you to show me the working out?

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#4

(Original post by

Is this what you mean : sin(x)cos(30)+cos(x)sin(60)=0.5 ?

I don't understand what to do next.

Is it possible for you to show me the working out?

**T933263**)Is this what you mean : sin(x)cos(30)+cos(x)sin(60)=0.5 ?

I don't understand what to do next.

Is it possible for you to show me the working out?

sin(x+60), on its own, is equivalent to sin(x)cos(60) + cos(x)sin(60). Do you see how the identity gets you from sin(x+30) to that?

and then cos(x+30) becomes cos(x)cos(30) - sin(x)sin(30) if you follow the angle addition formula for cosines.

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(Original post by

You haven't applied the identity correctly.

sin(x+60), on its own, is equivalent to sin(x)cos(60) + cos(x)sin(60). Do you see how the identity gets you from sin(x+30) to that?

and then cos(x+30) becomes cos(x)cos(30) - sin(x)sin(30) if you follow the angle addition formula for cosines.

**Sinnoh**)You haven't applied the identity correctly.

sin(x+60), on its own, is equivalent to sin(x)cos(60) + cos(x)sin(60). Do you see how the identity gets you from sin(x+30) to that?

and then cos(x+30) becomes cos(x)cos(30) - sin(x)sin(30) if you follow the angle addition formula for cosines.

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#6

(Original post by

I understand that part. Thanks. But what would I do next?

**T933263**)I understand that part. Thanks. But what would I do next?

I think after that the next step is factorising and converting it into the form if it doesn't simplify easily.

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#7

Having worked through it, you don't need to do anything complicated like that. It simplifies quite nicely.

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