Question

How to find the exact value using the Half-Angle Identity: 7pi/8 I am stuck

Answer 1

For what trigonometric function? sine cosine or what ?

Answer 2

tan

Answer 3

So far I get = \[\frac{ 1-\sqrt{2} }{ 1+\sqrt{2} }\]

Answer 4

is that right?

Answer 5

tan(157.5 )= tan (315 / 2 )

\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1-cos(a)}{1+cos(a)} } }\)

I need to check...

Answer 6

\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1-cos(315)}{1+cos(315)} } }\)

cos (315)= cos(360-45)=cos 360 cos 45 - sin 360 sin 45 =
cos 360=1
sin 360 = 0

cos 360 cos 45 - sin 360 sin 45 = 1 * cos 45 - 0 * sin 45 = cos 45

cos45=1/2


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1-1/2}{1+1/2} } }\)

Answer 7

\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1-1/2}{1+1/2} } }\)


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{2/2-1/2}{2/2+1/2} } }\)


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1/2}{3/2} } }\)


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1}{2} \div \frac{3}{2} } }\)


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1}{2} \times \frac{2}{3} } }\)


\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1}{3} } }\)

Answer 8

\(\Huge\color{blue}{ \bf ± \sqrt{ \frac{1}{3} } }\)

\(\Huge\color{blue}{ \bf ± \frac{ \sqrt{1}}{ \sqrt{3}} }\)

\(\Huge\color{blue}{ \bf ± \frac{ 1}{ \sqrt{3}} }\)

\(\Huge\color{blue}{ \bf ± \frac{ \sqrt{3}}{ 3} }\) is the ans.

Answer 9

but it says the answers can only be

1 + square root of two

1 - square root of two

-1 + square root of two

-1 - square root of two