Question

Help me solve tan 22.5 using the half angle theorem

Answer 1

http://www.regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm
Let (1/2)(A) = 22.5 degrees
Therefore, A = 45 degrees
tan(0.5 * 45) = (1- cos45)/sin45
I know the value is positive because the angle is in the 1st quadrant:
sin45 = cos45 = (sqrt2)/2

tan(0.5*45) =
(1- (sqrt2)/2)/((sqrt2)/2)

Answer 2

is it with 1+cos45 on the bottom?

Answer 3

sin45. If you look at the website, the half angle formula for tan can be expressed in 3 different ways, which are all the same.

Answer 4

so it would be \[\sqrt{1-\cos45\frac{ 1}{\cos 45 }}\]

Answer 5

pretend that the thing is next to the 1/45

Answer 6

so it would be \[1-\frac{ \sqrt{2} }{ 2 }\]

Answer 7

\[1+\frac{ \sqrt{2} }{ 2 }\]

Answer 8

?

Answer 9

It would be:
\[( 1-\sqrt{2}/2)/(\sqrt2/2)\]