HSC Stuff > HSC Mathematics Extension 1

3U Trig

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RuiAce:
Let me just add something here.

This sort of stuff is GENERALLY considered "Harder 3U" material for the 4U course. It is very unlikely that it should be examinable.


The more common thing to do is what ellipse said; apply a sum-to-product formula. But 3U students are, in general, without HELP, NOT expected to know the sum-to-product formulae off by heart. Only 4U students are 'expected' to memorise these procedures.

(Even then, I've only seen it appear once, which was in my trial HSC for MX2)

prabhleenkaur~:

--- Quote from: kiwiberry on January 22, 2017, 05:56:22 pm ---sinx + 2sinxcosx + 3sinx - 4sin3x = 0
2sinx(2 + cosx - 2sin2x) = 0
2sinx[-2(1-cos2x) + cosx + 2) = 0
sinx(2cos2x + cosx) = 0
sinxcosx(2cosx +1) = 0
therefore sinx=0, cosx=0 or cosx=-1/2

sinx = 0 = sin0
∴ x = πn

cosx = 0 = cos(π/2)
∴ x = 2πn ± π/2

cosx = -1/2 = cos(2π/3)
∴ x = 2πn ± 2π/3

--- End quote ---

Thank youuu!! Appreciate it!

prabhleenkaur~:

--- Quote from: jamonwindeyer on January 22, 2017, 06:48:07 pm ---Thanks kiwiberry, you are a legend!! ;D prabhleenkaur~, welcome to the forums! ;D

--- End quote ---

Glad to be a part of this ATAR Notes journey :D

armtistic:

--- Quote from: hanaacdr on January 23, 2017, 04:01:20 pm ---Hi
i have a similar question,
would i be able to get some help on this,

sin2x + sin3x + sin4x = 0

much appreciated thank you!

--- End quote ---


Rewrite it as

sin(3x-x) + sin3x + sin(3x+x) =0

Expand those and you get

2sin3xcosx+sin3x=0

sin3x(2cosx+1)=0

Solve sin3x=0 and 2cosx+1=0

x=kπ/3

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