Asked by kath
why does supplementary angles always have the same sin?
Answers
Answered by
Steve
use the difference formula:
sin(π-x) = sinπ cosx - cosπ sinx
sinπ=0 and cosπ = -1, so you wind up with
0 - (-1)(sinx) = sinx
Also, if you draw the angles in standard position, recall that
sinθ = y/r
cosθ = x/r
since y is positive in QI and QII, the two angles have the same sine value.
This also shows why cos(π-x) = -cosx -- x is negative in QII.
sin(π-x) = sinπ cosx - cosπ sinx
sinπ=0 and cosπ = -1, so you wind up with
0 - (-1)(sinx) = sinx
Also, if you draw the angles in standard position, recall that
sinθ = y/r
cosθ = x/r
since y is positive in QI and QII, the two angles have the same sine value.
This also shows why cos(π-x) = -cosx -- x is negative in QII.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.