Find the exact value. Use a sum or difference identity.

sin(-105˙)

Question

Find the exact value. Use a sum or difference identity.

sin(-105˙)

mattfeury · Answer

-105 degrees = 255 degrees

255˙ - 180˙= 75˙, so this is a 75 degree angle in the 3rd quadrant of the unit circle, meaning x and y are both negative.

anonymous · Answer

Omg, thank you so muchh! :D

mattfeury · Answer

no problem. please give medals to answerers that are helpful :)

so sin(-105˙) = - sin(75˙)

anonymous · Answer

Thankss!!!

anonymous · Answer

Wait, but then what is sin(75˙) ?

mattfeury · Answer

you can use the half angle identity, just like here: http://www.schooltrainer.com/homework-answers/use-a-half-angle-identity-to-find-the-exact-value-sin75-degrees

anonymous · Answer

That helps but I have to use the Angle Sum/Difference Identities.

anonymous · Answer

Don't know how Mathematica did it but here is what you will have to shoot for:
$$\text{Sin}[-105\text{Degree}]=-\frac{1+\sqrt{3}}{2 \sqrt{2}} $$