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Hey

Recently I have been studying for an upcoming test where it requires me to use “The “t” Method”. In this method the value of x for trigonometric equations is determined through vair the key component of “The “t” Method” is:

[tex]t=tan \frac{A}{2}[/tex]

[tex]tan A=\frac{1+t^2}{1-t^2}[/tex]

[tex]sin A=\frac{2t}{1+t^2}[/tex]

[tex]cos A=\frac{1-t^2}{1+t^2}[/tex]

If this is famliar to a reader by another name, could you please post this methods other name.

__________________________________________________Problems which i need to solve:

1. [tex]2sin x + 3cos x = 5[/tex]

2. [tex]3tan x + \sqrt{3}sec x=1[/tex]

3. [tex]10cos (pi x) + 3sin (2pi x)=4[/tex]

4. [tex]3sin 2x + 5cot 3x = 7[/tex]

5. [tex]csc x + 2sec (pi x)[/tex]

__________________________________________________My working for question 1. [tex]2sin x + 3cos x = 5[/tex]

[tex]2\frac{2t}{1+t^2} + 3\frac{1-t^2}{1+t^2} = 5[/tex]

[tex]\frac{4t + 3 - 3t^2}{1+t^2} = 5[/tex]

[tex]4t + 3 -3t^2 = 5 +5t^2[/tex]

[tex]4t + 2t^2 = 2[/tex]

[tex]2t^2 + 4t - 2 = 0[/tex]

[tex]t = 0.4142135624[/tex] or [tex]t = -2.414213562[/tex]

[tex]t = \tan\frac{x}{2}[/tex]

[tex]x = 2tan^-1 0.4142135624[/tex] or [tex]x = 2tan^-1 -2.414213562[/tex]

[tex]x = 45[/tex] or [tex]x = -135.0005034[/tex]

__________________________________________________I conclude my working here as I am not sure if it is correct. Is there an aleternaitve method I could use to check these final answers? And are there any more values of x for which the equation is true?

Thanks well in advance,

Pavadrin

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# Homework Help: The t Method

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