Sin(theta + pi/3) signifies a translation of pi/3 in the x-axis of the sine graph meaning that the graph shifts to the left. It is not an algebraic function.

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There is an addition formula for sin (and cos) which allows you to expand things like sin(A+B) in terms of sinA, cosA, sinB and cosB, so the method would work perfectly well!

In this case it's complete overkill because you can work out tan(pi/6) without a calculator and then just solve like a normal trig equation.

Reply 22

Sena5

20

Original post by Cool-Light

expanding LHS gives me => sin theta + sin pi/3 = tan pi/6 - what now?

The rule is you should never expand sin,cos or tan because they are functions. you cant and shouldn't because that is a rule.

(edited 9 years ago)

Reply 23

Smaug123

15

Original post by kers123

The rule is you should never expand sin,cos or tan because they are functions. you cant and shouldn't because that is a rule.

That's not a very good reason for not being able to expand sin,cos or tan. (By "expand" you mean "sin(a+b) is not sin(a)+sin(b)".)

The actual reason why you can't expand sin, cos or tan is simply that it doesn't work.

\sin(\pi) + \sin(\frac{\pi}{2}) = 0 + 1 = 1

but

\sin(\pi+\frac{\pi}{2}) = \sin(\frac{3}{2} \pi) = -1

. There's no rule saying that it doesn't work - it just doesn't. It's like saying "you can't flap your arms and fly, that's a rule" - it's not really a rule, it just doesn't work.

Reply 24

Sena5

20

Original post by Smaug123

That's not a very good reason for not being able to expand sin,cos or tan. (By "expand" you mean "sin(a+b) is not sin(a)+sin(b)".)

The actual reason why you can't expand sin, cos or tan is simply that it doesn't work.

\sin(\pi) + \sin(\frac{\pi}{2}) = 0 + 1 = 1

but

\sin(\pi+\frac{\pi}{2}) = \sin(\frac{3}{2} \pi) = -1

. There's no rule saying that it doesn't work - it just doesn't. It's like saying "you can't flap your arms and fly, that's a rule" - it's not really a rule, it just doesn't work.

The rule tells we should not use it. It's wrong to use and that's how many students don't understand and lose marks in exams.

Reply 25

davros

16

Original post by kers123

The rule is you should never expand sin,cos or tan because they are functions. you cant and shouldn't because that is a rule.

That depends what you mean by "expand". There are perfectly good formulae that tell you how to expand sin(A+B), cos(A+B) and tan(A+B) in terms of other quantities.

What you're trying to say is that sin isn't a linear function i.e.

sin(A+B) \neq sin A + sin B

Reply 26

Sena5

20

Original post by davros

That depends what you mean by "expand". There are perfectly good formulae that tell you how to expand sin(A+B), cos(A+B) and tan(A+B) in terms of other quantities.

What you're trying to say is that sin isn't a linear function i.e.

sin(A+B) \neq sin A + sin B

Exactly!

Examiner's cut out marks if they expand this way.

Students should not expand this way.

Instead she can use her calculator to get a value for tan ...
and solve normally

(edited 9 years ago)

Reply 27

Smaug123

15

Original post by kers123

Exactly!

Examiner's cut out marks if they expand this way.

Students should not expand this way.

Instead she can use her calculator to get a value for tan ...
and solve normally

I do think this is a strange way to think about maths. The reason you can't expand this way isn't that "examiners don't like it", it's that "it makes no sense".

Consider the following example: a student asserts that 5+5=6; you reply that if you do that then the examiners will dock marks, and there is a rule against saying "5+5=6". Yes, that's true, but it's not *why* you can't do 5+5=6 - the fact that examiners dock marks is a *symptom* of the fact that "5+5=6 is nonsense", not a cause.