We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

#3**+10 **

Great work Chris and Geno.

I'm going to hit it a different way.

$$\\\tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}\\\\

\tan(2x)=\frac{2tanx}{1-tan^2x}\\\\\\$$

so draw a right angled triangle and make one of the acute angles = 2x

the opposite side is $$2tanx=2*2=4$$

the adjacent side is $$1-tan^2x=1-2^2=1-4=-3$$ (the negative sign just means it will not be in the first quad )

Using pythagoras the hypotenuse will be

$$\\h=\sqrt{4^2+(-3)^2}\\

h=\sqrt{16+9}\\

h=\sqrt{25}\\

h=5\\$$

so

$$\\cos(2x)

=\frac{adj}{hyp}

=\frac{-3}{5}

=\;-0.6$$

Melody Oct 7, 2014

#1**+5 **

If tan(x) = 2, the x = 63.435°.

cos(2x) = cos(2·63.435°) = cos(126.870°) = -0.6

This can also be done without a calculator, if you need that explanation, please repost.

geno3141 Oct 6, 2014

#2**+10 **

If tan x = 2, then y / x = 2 / 1

Then, using, √(x^{2} + y^{2} ) = r^{ }

√(2^{2} + 1^{2}) = √5 = r

So sin x = y/r = 2/√5

And using

cos 2x = 1 - 2(sin x)^{2}

cos 2x = 1 - 2(2/√5)^{2}

cos 2x = 1 - 2 (4/5)

cos 2x = 1 - 8/5

cos 2x = -3/5 = -(.6) .....as geno found !!!!!!!

CPhill Oct 6, 2014

#3**+10 **

Best Answer

Great work Chris and Geno.

I'm going to hit it a different way.

$$\\\tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}\\\\

\tan(2x)=\frac{2tanx}{1-tan^2x}\\\\\\$$

so draw a right angled triangle and make one of the acute angles = 2x

the opposite side is $$2tanx=2*2=4$$

the adjacent side is $$1-tan^2x=1-2^2=1-4=-3$$ (the negative sign just means it will not be in the first quad )

Using pythagoras the hypotenuse will be

$$\\h=\sqrt{4^2+(-3)^2}\\

h=\sqrt{16+9}\\

h=\sqrt{25}\\

h=5\\$$

so

$$\\cos(2x)

=\frac{adj}{hyp}

=\frac{-3}{5}

=\;-0.6$$

Melody Oct 7, 2014