Question

Find the exact value by using a half-angle identity.

tangent of seven pi divided by eight.

Answer 1

\[\sin(x)=\sqrt{\frac{ 1-\cos(2x) }{ 2 }}\]\[\cos(x)=\sqrt{\frac{ 1+\cos(2x) }{ 2}}\]then\[\tan(x)=\sqrt{\frac{ 1-\cos(2x) }{ 1+\cos(2x) }}\] and\[\cos(2x)=\cos(7\pi/4)=\cos(2 \pi-\pi/4)=\cos(-\pi/4)=\cos(\pi/4)=\frac{ \sqrt{2} }{ 2 }\]Then you have:\[\tan(7\pi/8)=\sqrt{\frac{ 2-\sqrt{2} }{ 2+\sqrt{2}}}=0.4142\]Now pay attention to the sign as 7*pi/8 is in the second quadrant, then its tangent has to be negative. Then your solution is:-0.4142

Answer 2

oh wow so the answer is -0.4142?

Answer 3

exactly, check it with your calculator

Answer 4

kk wil do one sec I did that horribly wrond then -_-

Answer 5

sure as poopits right thank you so much

Answer 6

u r w