Question

medal!!!!
use a half angle identity to find the exact value of sin 105 degree

Answer 1

HI!!

Answer 2

\[105\] is half of \(210\) right ?

Answer 3

you are going to use
\[\sin(105)=\sqrt{\frac{1-\cos(210)}{2}}\]

Answer 4

so what you need is to find \(\cos(210)\)

Answer 5

hey

Answer 6

its - squared 3/2

Answer 7

\(\large\color{slate}{ \sqrt{~~~~~} }\) is called a square root.
"squared" is when you raise a number to a second power.

Answer 8

yes it is

Answer 9

sorry my bad;/

Answer 10

`\(\large\color{slate}{ \sqrt{ } }\)`

Answer 11

sure:)

Answer 12

so you get
\[\sqrt{\frac{1+\frac{\sqrt3}{2}}{2}}\]

Answer 13

Also, you can use my latex: `\(\large\color{slate}{ \displaystyle -\frac{\sqrt{3}}{2} }\)`

\(\large\color{slate}{ \displaystyle -\frac{\sqrt{3}}{2} }\)

Answer 14

simplify this complex fraction by multiplying inside top and bottom by \(2\)

Answer 15

6/2=3/1?

Answer 16

hmm i guess i confused you

Answer 17

inside the radical is
\[\frac{1+\frac{\sqrt3}{2}}{2}\]

Answer 18

to get rid of the compound fraction, multiply top and bottom by 2

Answer 19

2 + 0.86/4

Answer 20

@misty1212

Answer 21

your answers do not use decimal approximations
leave the radical there

Answer 22

\[\sqrt{\frac{2+\sqrt3}{4}}\] or
\[\frac{1}{2}\sqrt{2+\sqrt3}\]

Answer 23

thanks so much!!

Answer 24

@misty1212 thanks

Answer 25

\[\color\magenta\heartsuit\]