Half Angle Formulas

• Mar 17th 2010, 05:56 AM
purplec16
Half 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 AM
sa-ri-ga-ma
Quote:

Originally Posted by purplec16
Can someone please help me with this question I need it in like 10-20 mins

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

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

If 3π/8 = θ, then 3π/4 = 2θ
Now tan(2θ) = 2*tanθ/(1-tan^2θ)........(1)

tan(2θ) = tan(3π/4) = ..........?
Substitute this value in the eq.(1) and solve for tanθ
• Mar 17th 2010, 06:25 AM
purplec16
Quote:

Originally Posted by sa-ri-ga-ma
If 3π/8 = θ, then 3π/4 = 2θ
Now tan(2θ) = 2*tanθ/(1-tan^2θ)........(1)

tan(2θ) = tan(3π/4) = ..........?
Substitute this value in the eq.(1) and solve for tanθ

I need to solve it using one of the half-angle formulas
• Mar 17th 2010, 05:50 PM
sa-ri-ga-ma
Quote:

Originally Posted by purplec16
I need to solve it using one of the half-angle formulas

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 PM
skeeter
$\displaystyle \tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos{\theta}}{1+\cos{\theta}}}$

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.