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Find the exact value by using a halfangle identity.
tan7π/8
PLEASE PLEASE PLEASE :)
 one year ago
 one year ago
Find the exact value by using a halfangle identity. tan7π/8 PLEASE PLEASE PLEASE :)
 one year ago
 one year ago

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wioBest ResponseYou've already chosen the best response.1
Well, the half angle identity says: \[ \sin(\theta/2) = \sqrt{\frac{1\cos(\theta)}{2}} \quad \cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}} \]
 one year ago

wioBest ResponseYou've already chosen the best response.1
Well \[ \tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)} \]So I didn't really remember it's identity for this. Rather, I just divided the other identities.
 one year ago

wioBest ResponseYou've already chosen the best response.1
So then \[ \tan(\theta / 2) = \sqrt{\frac{1\cos(\theta)}{1+\cos(\theta)}} \]
 one year ago

glucy7Best ResponseYou've already chosen the best response.0
well i just don't really understand how to do the problem once everything is plugged in
 one year ago

wioBest ResponseYou've already chosen the best response.1
Well, \(\cos(7\pi/4)\) is relatively easy to solve for, when you look at the unit circle.
 one year ago

glucy7Best ResponseYou've already chosen the best response.0
well i know how to find the degree but once i get the degree i dont know where to go from there
 one year ago

Rosh007Best ResponseYou've already chosen the best response.0
that is a good method... but tan's identity is below \[\large \tan (\frac{ \theta }{ 2 }) =\frac{ \sin(\theta) }{1+ \cos (\theta) }=\frac{ 1 \cos (\theta) }{\sin(\theta) }\]
 one year ago

glucy7Best ResponseYou've already chosen the best response.0
do you mind just showing me the steps please??
 one year ago

glucy7Best ResponseYou've already chosen the best response.0
can you use the half angle formula
 one year ago

wioBest ResponseYou've already chosen the best response.1
yes, if you consider 7pi/8 to be a half angle, then that means the full angle is 7pi/4
 one year ago

wioBest ResponseYou've already chosen the best response.1
Since for 7pi/4 it is easy to find the values of sin/cos, it is useful here.
 one year ago

wioBest ResponseYou've already chosen the best response.1
Think of it this way, 7pi/4 is pi/4 short of 2pi. 2pi is a full circle. So pi/4 is just a quarter of a circle.
 one year ago

wioBest ResponseYou've already chosen the best response.1
What makes a quarter of a circle easy to calculate, is the fact that the you know the the horizontal and vertical part are equal, so I set them to a and solved for a to find the value of cos
 one year ago

wioBest ResponseYou've already chosen the best response.1
\(a^2+a^2=1\) is just Pythagorean theorem.
 one year ago
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