Question

Use a half–angle identity to find the exact value of sin 105°.

Answer 1

105=60+?

Answer 2

105=60+45

Answer 3

now we use \[\sin (A+B)=\sin Acos B+\sin Bcos A\]

Answer 4

wait the question says half angle this is compound angle

Answer 5

sin(60+45) = sin60cos45 + sin60cos45

Answer 6

this way will work but the question is looking for the 1/2 angle identity

Answer 7

oh my gosh! YES! hahaha tats what i cant figure out the half angle identity to use for this problem.

Answer 8

*thats

Answer 9

\[\sin(A)=\sqrt{\frac{ 1-\cos 2A }{ 2 }}\]

Answer 10

so let A=105 then 2A=210

Answer 11

so it would be -1/2 radical 2+radical 3 ?

Answer 12

2+radical3 being under a radical

Answer 13

if you have a calculator find cos(210) or you rewrite it as cos(180+30)="-(sqrt(3)/2)".
So plugging this value into jonask's equation will give you the answer

Answer 14

1/2 2+radical 3 . thats my answer

Answer 15

this one is right :) \[\sqrt{2+\sqrt{3}}\div2 \]

Answer 16

so i was close ! :) thank you !

Answer 17

your welcome.. gud bye..