HSC Stuff > HSC Mathematics Extension 1

Trigonometry

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Jefferson :
Hi all, for the questions below, I'm a little stuck on part ii. (attachment)

For part i. , I did

2 sinx cosx = 2 sin2x
sin2x -  sinx cosx = 0
sinx ( sinx - cosx ) = 0

sin x = 0
{0 < x < π}
No solution for sinx = 0 in domain.

sinx =cosx
tanx = 1 (divide by cosx, is there anything mathematically wrong with this and I can't use it, i.e. x ≠ π/2?)
{0 < x < π}
x = π/4 is the only solution.

Would you have done anything differently?
Please help me with part ii.

Thank you.

fun_jirachi:

--- Quote from: Jefferson  on March 19, 2019, 09:50:01 pm ---sinx =cosx
tanx = 1 (divide by cosx, is there anything mathematically wrong with this and I can't use it, i.e. x ≠ π/2?)
{0 < x < π}
x = π/4 is the only solution.

--- End quote ---

This seems fine. Considering the graphs of cos x and sin x should also give you a better idea ie. they intersect at x=(4n+1)pi/4, so within this domain the only solution is pi/4.

For part ii, since you have proven that they intersect at pi/4 and zero, consider the graphs of both these functions. Graphing both of these should make the result pretty obvious to you. Hope this helps :)

Jefferson :

--- Quote from: fun_jirachi on March 19, 2019, 10:06:32 pm ---This seems fine. Considering the graphs of cos x and sin x should also give you a better idea ie. they intersect at x=(4n+1)pi/4, so within this domain the only solution is pi/4.

For part ii, since you have proven that they intersect at pi/4 and zero, consider the graphs of both these functions. Graphing both of these should make the result pretty obvious to you. Hope this helps :)

--- End quote ---

Hi, fun_jirachi.
For part ii.
Is there an algebraic approach to this question, or is graphing both functions on the same axis the only way?
Thanks for answering!

fun_jirachi:
Above you also proved that in that domain, there are no solutions ie. one graph is always above the other. Therefore, you can also just test a point for both curves to see which one is greater than the other over that domain. Not too sure about an algebraic approach for this. Hope this helps anyway! :)

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