Question

What is the exact value of sin(195°)?

A. (√2 + √6)/4

B. (√6 - √2)/4

C. (√2 - √6)/4

D. (√6 - √3)/4

Answer 1

I got (√6 - √2)/4 which is B.)

Answer 2

\[\sin195=\sin(180+15)=\sin180\cos15+\cos180\sin15=-\sin15\]
\[\cos30=1-2\sin^{2}15\]
\[2\sin^{2}15=1-\cos30=1-\frac{ \sqrt{3} }{ 2 }\]
\[\sin195=-\sqrt{\frac{ 1 }{2 }+\frac{ \sqrt{3} }{ 4 }}\]

Answer 3

\[\sin 195=\sin(150+45)=\sin150\cos 45+\cos 150\sin 45\]
\[=\sin (180-30)\cos 45+\cos (180-30)\sin 45\]
\[=\sin 30\cos 45-\cos 30\sin 45\]
\[=\frac{ 1 }{ 2 }(\frac{ \sqrt{2} }{ 2 })-\frac{ \sqrt{3} }{ 2 }(\frac{ \sqrt{2} }{ 2})\]
\[=\frac{ \sqrt{2} }{ 4}-\frac{ \sqrt{6} }{ 4}=\frac{ \sqrt{2}-\sqrt{6} }{ 4}\]
so C

Answer 4

Hmmmmmm interesting thanks