Find the exact value of tan 13π/8 using half-angle identities.
sqrt(2)-sqrt(3)/2
-sqrt(2)-1
1-sqrt(2)
sqrt(2)-sqrt(2)/2
possible answers

Question

Find the exact value of tan 13π/8 using half-angle identities.
sqrt(2)-sqrt(3)/2 
-sqrt(2)-1
 1-sqrt(2)
 sqrt(2)-sqrt(2)/2
possible answers

anonymous · Answer

i guess $\frac{13\pi}{8}$ is half of $\frac{13\pi}{4}$

anonymous · Answer

sqrt(2)-sqrt(3)/2 
-sqrt(2)-1
 1-sqrt(2)
 sqrt(2)-sqrt(2)/2
possible answers

anonymous · Answer

oh ok so that half 13x/4?

anonymous · Answer

perhaps easiest to use 
$$\tan(\frac{13\pi}{8})=\frac{\sin(\frac{13\pi}{4})}{1+\cos(\frac{13\pi}{4})}$$

anonymous · Answer

yes $\frac{13\pi}{8}$ is half of $\frac{13\pi}{4}$

anonymous · Answer

so what the next step to getting the possible answer i listed

anonymous · Answer

sqrt(2)-sqrt(3)/2 
-sqrt(2)-1
 1-sqrt(2)
 sqrt(2)-sqrt(2)/2

anonymous · Answer

the last step is to compute $\frac{\sin(\frac{13\pi}{4})}{1+\cos(\frac{13\pi}{4})}$ and see what you get

anonymous · Answer

i got 1.16 rounded but it doesnt match the other answes so is there something im missing

anonymous · Answer

since $\frac{13\pi}{4}$ is coterminal with $\frac{3\pi}{4}$ you can find $\sin(\frac{3\pi}{4})$ and $\cos(\frac{3\pi}{4})$ instead
don't use a calculator, write down the exact answer

anonymous · Answer

oh ok soo use sin=135 and cos 135 too so -sqrt(2)/2  sqrt(2)

anonymous · Answer

oh ok soo use sin=135 and cos 135 too so -sqrt(2)/2  sqrt(2)/2

raden · Answer

13pi/4 - 2pi = 5pi/4
i think u can use 5pi/4 or 225 degrees not 135 d...

anonymous · Answer

oh so use 225 so what do i do next?

anonymous · Answer

oh damn you are right sorry

anonymous · Answer

it is coterminal with $\frac{5\pi}{4}$

anonymous · Answer

forget about degrees, you are an adult and so you should only use them if you are "solving" a triangle
you need to know that $\cos(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$ and also $\sin(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$

anonymous · Answer

so they answer but it doesnt match any of my answers ?? so idk

anonymous · Answer

$$-\frac{\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}$$

anonymous · Answer

simplify by multiplying top and bottom by 2

anonymous · Answer

$$\frac{-\sqrt{2}}{2-\sqrt{2}}$$

anonymous · Answer

the answer 2? if u simplfy

anonymous · Answer

multiply by conyugate of denominator...

anonymous · Answer

huh so multpy by sqrt 2

anonymous · Answer

no, but multiply  (2+sqrt(2))/(2+sqrt(2)

anonymous · Answer

1 right

anonymous · Answer

not yet

anonymous · Answer

???

anonymous · Answer

can u simplify it :
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