Question

angle sum&angle difference
sin(-105*)

Answer 1

whats the question?

Answer 2

you're suppose to evaluate using angle sum and angle diffeence formulas

Answer 3

the negative is what threw me off

Answer 4

how does -105 degrees = 255 degrees? @lhxza2

Answer 5

i still do not understand. Which of the sum and difference formulars do I use beeing that the degree is negatrive?

Answer 6

If we want to use angle diffirence formula, we should probably write our angle like this
\[\Large\rm -105=-45-60\]
k? :)

Answer 7

i see

Answer 8

And then it makes it easier to use our formula!\[\Large\rm \sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\sin(\beta)\cos(\alpha)\]

Answer 9

okay I was not sure , thanks

Answer 10

understand how to finish it up? :o
Good with your special angles like these? \(\Large\rm \cos(-45)\)

Answer 11

one sec

Answer 12

okay so it would be : sin-60cos-45-sin-45cos-60?@zepdrix

Answer 13

@zepdrix

Answer 14

Woops, if we're using the DIFFERENCE formula, then keep in mind that your second value, the beta is 60, not -60.

Answer 15

\[\Large\rm \sin\left(-105\right)=\sin\left(\color{orangered}{-45}-\color{royalblue}{60}\right)\]

Answer 16

\[\Large\rm =\sin(\color{orangered}{-45})\cos(\color{royalblue}{60})-\sin(\color{royalblue}{60})\cos(\color{orangered}{-45})\]

Answer 17

okay so would the negatie affect the ordered pairs on the unit circle?

Answer 18

Mmm yes I suppose it would since \(\Large\rm \sin(-60)\ne\sin(60)\)
So yes, the negative sign is important, if that's what you're asking :o

Answer 19

how will i simplify the formula?

Answer 20

after my values have been subd. in?

Answer 21

Mmmm you need to use your unit circle I suppose D:
Oh oh this might help a little bit, hopefully we're allowed to do this.
Since cosine is an `even function`:\[\Large\rm \cos(-\alpha)=\cos(\alpha)\]And since sine is an `odd function`:

Answer 22

\[\Large\rm \sin(-\beta)=-\sin(\beta)\]

Answer 23

So the negative comes out of the sines, and it disappears for the cosines.\[\Large\rm =\sin(\color{orangered}{-45})\cos(\color{royalblue}{60})-\sin(\color{royalblue}{60})\cos(\color{orangered}{-45})\]\[\Large\rm =-\sin(45)\cos(60)-\sin(60)\cos(45)\]

Answer 24

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png

Cosine is the `x coordinate` of the ordered pair,
while Sine is the `y coordinate` of the ordered pair.