find exact value of tan(255) using half angle identity for tangent. Half angle identity is tan(a/2) but i want to approach this problem with finding two angles that I know like 225 degrees + 30 degrees. Any ideas?

Question

solomonzelman · Answer

Do the half angle man !!

$\large\color{blue}{ \bf     tan(255)=tan(510/2)=±\sqrt{  \frac{1-cos(510)}{1+cos(510)}  } 	 }$

$\large\color{blue}{ \bf    ±\sqrt{  \frac{1-cos(510)}{1+cos(510)}  } =\frac{1-cos(510)}{sin(510)}	 }$

solomonzelman · Answer

cos(510)=cos(480+30)=cos(480)cos(30)-sin(480)sin(30) = ?
sin(510)=sin(480+30)=sin(480)cos(30)+cos(480)sin(30) = ?

go for it....

anonymous · Answer

Awesome I didn't see that 510/2 = 255 which puts me at cords. $$(-\sqrt{3})/2, 1/2)$$

anonymous · Answer

Thank you!!!

anonymous · Answer

$$(-\sqrt{3}/2, 1/2)$$ somehow an extra ")" got in there.

solomonzelman · Answer

Looks right, I just don;t know the values of sin, cos 480 

I know that  sin(30)=1/2  and  cos(30=√3 / 2 
(each time I forget the 30º sine and cosine, but then draw a 30-60-90 triangle and apply sohcahtoa) ....

have a good night....

anonymous · Answer

same to you.