$\displaystyle tan \frac{3\pi}{8}$

Use $\displaystyle tan 2\theta$ to find the exact value

Im stuck because I dont know which half-angle formula do I use?

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- Mar 17th 2010, 05:56 AMpurplec16Half Angle Formulas
$\displaystyle tan \frac{3\pi}{8}$

Use $\displaystyle tan 2\theta$ to find the exact value

Im stuck because I dont know which half-angle formula do I use? - Mar 17th 2010, 06:12 AMsa-ri-ga-ma
- Mar 17th 2010, 06:25 AMpurplec16
- Mar 17th 2010, 05:50 PMsa-ri-ga-ma
I have given the half angle formula.

If 2θ = 3π/4, half of that angle is θ = 3π/8 which is the required angle.

I have observed that you are not following our instructions. Every time you expect the complete solution. It is not good for any student who wants to study the subject.

In my post, you have to find the value of tan(3π/4), simplify the expression, solve the quadratic equation to get tanθ, i.e. tan(3π/8).

Can you try now? - Mar 17th 2010, 06:02 PMskeeter
$\displaystyle \tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos{\theta}}{1+\cos{\theta}}}$

if $\displaystyle \frac{\theta}{2} = \frac{3\pi}{8}$ , then $\displaystyle \theta = \frac{3\pi}{4}$

also note that $\displaystyle \frac{3\pi}{8}$ is a quad I angle, so $\displaystyle \tan\left(\frac{3\pi}{8}\right) > 0

$

plug and chug using the given half-angle formula.