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kalli
 one year ago
Use the halfangle formula to evaluate tan(17pi/12)
kalli
 one year ago
Use the halfangle formula to evaluate tan(17pi/12)

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2well \[\tan(\frac{17\pi}{12}) \\ y=\tan(x) \text{ has period } \pi \\ \tan(\frac{17\pi}{12}\pi)=\tan(\frac{17\pi}{12}\frac{12\pi}{12})=\tan(\frac{5\pi}{12}) \\ \text{ now } 2 \cdot \frac{5 \pi}{12}=\frac{5\pi}{6} \\ \text{ so we have that we want to use the halfangle formula on } \\ \tan( \frac{1}{2} \cdot \frac{5 \pi}{6})\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2do you know the half angle identity for tan?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so you can't use the half angle identity for tan?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you can only use the one for sin?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2the weird thing is you have tan here not sin

freckles
 one year ago
Best ResponseYou've already chosen the best response.2or do you mean you can use it but you just don't know it?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2http://www.purplemath.com/modules/idents.htm do you see halfangle identities on this page?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2notice the three different ones they wrote for tan(x/2)

kalli
 one year ago
Best ResponseYou've already chosen the best response.0im confused because I don't really know how to do this lol

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well first let's just copy of of the halfangle identities over from that page \[\tan(\frac{1}{2}x)=\frac{\sin(x)}{1+\cos(x)} \\ \text{ and we want to evaluate } \\ \tan(\frac{1}{2} \frac{5\pi}{6})=?\] do you see what to replace x with ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2compare tan(1/2*5pi/6) to tan(1/2*x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2x has to be 5pi/6 right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so replace the x's in the identity with 5pi/6

kalli
 one year ago
Best ResponseYou've already chosen the best response.0tan(1/2*5pi/6)= sin(5pi/6) / 1+cos(5pi/6) ??

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ok and ( ) around the bottom

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so sin(5pi/6)=? and cos(5pi/6)=?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\tan(\frac{1}{2} \cdot \frac{5\pi}{6})=\frac{\frac{1}{2}}{1+\frac{\sqrt{3}}{2}}\] multiply top and bottom by 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{\frac{2}{2}}{2+\frac{2(\sqrt{3})}{2}}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2can you simplify from there?

kalli
 one year ago
Best ResponseYou've already chosen the best response.0@freckles is that my answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{\frac{2}{2}}{2+\frac{2(\sqrt{3})}{2}} \\ \frac{1}{2\sqrt{3} } \\ \frac{1}{2 \sqrt{3}} \cdot \frac{2 +\sqrt{3}}{2+\sqrt{3}} \\ \frac{2+\sqrt{3}}{43} \\ \frac{2 +\sqrt{3}}{1} \\ 2+\sqrt{3}\]
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