Question

Select the matching value for y in each function WITHOUT a calculator.

Answer 1

\[y=\sin \left( -240 \right)\]

Answer 2

Hint: Use this unit circle

http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png

Answer 3

keep in mind that -240 is coterminal to -240+360 = 120 degrees

Answer 4

but what about the negative...thats kinda whats throwing me

Answer 5

so sin(-240) = sin(120)

Answer 6

oh k so it's sqrt3/2 then! :D awesome,
is the only way to figure these types of questions out with either a calculator or that unit circle?

Answer 7

pretty much, or you can memorize or have a table

and yes, sin(120) = sqrt(3)/2

Answer 8

so theres no mathematical way to manage it.

Answer 9

unfortunately some calculators will only give you the decimal form, not the exact form

eg: some calculators would say that sin(120) = 0.866, but you would have no way of knowing that 0.866 = sqrt(3)/2

Answer 10

there is, but it would take quite a while to get it by hand and I don't think there's an easy way to get all exact answers

Answer 11

okay...cause my teacher asked us not to use a calculator so i'm not sure if she expects us to memorize a chart or to just deal with it...

Answer 12

however, for special triangles, like 30-60-90 triangles or 45-45-90 triangles, you can draw these figures

30-60-90 triangle




45-45-90 triangle