Quick trigonometry question (1 Viewer)

Leffife · Jun 24, 2012

The answer I got is -21/√7 but the answer at the back is 21/√7.

If sin θ = 3/4 , 90* < θ < 180*, evaluate in surd form:

tan 2θ

I'm just wondering now if the answer at the back is incorrect.

Deliriously · Jun 24, 2012

okay its in the second quadrant
so tanθ = -3/√7

tan(2θ) = (2tanθ)/(1-tan²θ)
= (-6/√7)/(-2/7)
= 21/√7

so the answer from the book was correct

Sy123 · Jun 24, 2012

Draw the triangle, do Pythagoras and you find:

$\tan{\theta}=\frac{-3}{\sqrt{7}} \ \ \ (\text{Since from}) 90 < \theta < 180 \ \ \ \tan{\theta}<0 \\ \\ \tan{2\theta}=\frac{2\tan{\theta}}{1-\tan^2{\theta}} \\ \\ \tan{2\theta}=\frac{2\times \frac{-3}{\sqrt{7}}}{1-\frac{9}{7}} = \frac{\frac{-6}{\sqrt{7}}}{\frac{-2}{7}} = \frac{21}{\sqrt{7}}$

Leffife · Jun 24, 2012

Deliriously said:
okay its in the second quadrant
so tanθ = -3/√7

tan(2θ) = (2tanθ)/(1-tan²θ)
= (-6/√7)/(-2/7)
= 21/√7

so the answer from the book was correct

ahh thanks, i can't believe i totally forgot about the domain... thanks man. I saw it but never payed attention to it.

Sy123 · Jun 24, 2012

As my math teacher always says, they never give anything in the question in vain.

Quick trigonometry question (1 Viewer)

Leffife

A lover is a best friend

Deliriously

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Sy123

This too shall pass

Leffife

A lover is a best friend

Sy123

This too shall pass

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