Question

Find the exact value of each expression: cos(105)

Answer 1

I need to work on studying for tomorrow's test.

Answer 2

\[\cos 105=\cos \left( 60+45 \right)=?\]

Answer 3

Yes, I can do the work real quick, one second.

Answer 4

\[\cos 60=\frac{ 1 }{ 2 },\sin 60=\frac{ \sqrt{3} }{ 2 }\]
\[\sin 60=\frac{ \sqrt{3} }{ 2 },\sin 45=\frac{ 1 }{ \sqrt{2} }\]

Answer 5

cos60cos45-sin60sin45
(1/2)(rad(3)/2) - (rad(3)/2)(1/rad(2)

Answer 6

\[\cos 45=\frac{ 1 }{ \sqrt{2} }\]

Answer 7

Oh okay, I was falling along with your representations.

Answer 8

no, i mistakenly wrote sin 60 twice.

Answer 9

Sorry for not using the tool thing on here, I just understand it even when I use less clear representations of it.

Answer 10

cos of 45 is rad(2)/2

Answer 11

1/2(rad(2)/2 - rad(3)/2 (rad(2)/2

Answer 12

rad(2)/4 - rad(6)/4

Answer 13

\[\frac{ 1-\sqrt{3} }{ 2\sqrt{2} }=\frac{ \sqrt{2}-\sqrt{6} }{ 4 }\]
you are correct.

Answer 14

Thanks man.

Answer 15

Are you pretty good with identities by chance? I really need to practice those.

Answer 16

\[\cos 45=\frac{ 1 }{ \sqrt{2} }=\frac{ \sqrt{2} }{ 2 }\]

Answer 17

i am Masters in mathematics.

Answer 18

Oh okay, sorry, I have my unit circle here, and I am more used to the other form. I forgot about that form.