can someone explain the principle values from the unit circle?

Question

anonymous · Answer

in complex functions you meant?

anonymous · Answer

no i mean on my homework it says provide exact values from the unit circle and simplfy the expression using the unit circle. ex: $$\sin^{-1} (-\sqrt{2}\div 2)$$

anonymous · Answer

the common angles on the unit circle?

anonymous · Answer

attachment

anonymous · Answer

like the first set of problems

anonymous · Answer

ok... what you wrote down is the same as asking:
sin(what angle) = -(sqrt2)/2
can you figure out the "what angle" part above?
look at your unit circle... sin refers to the y coordinates of those points on the circle.

anonymous · Answer

i understand

anonymous · Answer

so what's the angle?

anonymous · Answer

315 degrees?

anonymous · Answer

correct... somewhat....

anonymous · Answer

sine inverse has a range of (-90 degrees, 90 degrees).  you'll have to determine an angle in there that is coterminal with 315 degrees.

anonymous · Answer

|dw:1337373018828:dw|
give an angle between -90 and 90 that has the same terminal side as 315

anonymous · Answer

these are the principle values they're talking about.

anonymous · Answer

need help?

anonymous · Answer

yes please

anonymous · Answer

|dw:1337373193802:dw|
what angle is that?