Question

Use a half angle identity to find the exact value of the expression: sin105 degrees

Answer 1

well, sin(105) = sin(45+55) = (sin addition formula). But then we would still need the exact value of sin55.

But we can play the same trick using 55 = 45 + 10.

Answer 2

I have the formula sin u/2= +- radical 1-cos u/ 2 is that correct?

Answer 3

We can make it sin (60+45)

Answer 4

But how do I plug it into that formula? Or is that the correct formula?

Answer 5

What formula?
do you have specific formula?

Answer 6

@amandamv1994

Answer 7

It says to use half angle identity. But in my book it says half angle formula. Its sin u/2 =+- radical 1-cos u/2

Answer 8

I don't think you can use this formula here because you have to break the angle to known angles which are 0,30,45,60,90,180,270 or 360

Answer 9

Hm okay. Cause the answer is supposed to be \[\sqrt{2-\sqrt{3}}\div 2\]

Answer 10

do you have formula for sin(60+45) and how can you break it?

Did you take these stuff?

Answer 11

Is that the sin (u+v) ?

Answer 12

Addition and Subtraction Formulas
For Sine and Cosine
1. sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
2. sin(x – y) = sin(x)cos(y) − cos(x)sin(y)
3. cos(x + y) = cos(x)cos(y) − sin(x)sin(y)
4. cos(x – y) = cos(x)cos(y) + sin(x)sin(y)

Did you take those equations before?

Answer 13

Yes

Answer 14

we can apply the first one in your case here

Which is :

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

Answer 15

sin(60+ 45) = sin(60) cos(45) + cos(60) sin(45)

Answer 16

Then thats when we refer to the unit circle?

Answer 17

\[(\sqrt{3}/2)*(1/\sqrt{2}) + (0.5 * (1/\sqrt{2})\]

Answer 18

I guess so
I don't really remember the name but let's see if we get the same answer

Answer 19

Cause the points for 45 degrees is \[\sqrt{2/2, \sqrt{2/2}}\]