# trigonometry

why does supplementary angles always have the same sin?

1. 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.

posted by Steve

## Similar Questions

1. ### Geometry

Is the following definiiton of supplementary reversible? If yes, write it as a true biconditional. Supplementary angles are two angles whose measures sum to 180. a. Yes, if angles are supplementary, the their measures sum to 180.
2. ### Calculus - Challenge question

Our teacher gave us this problem as a challenge. Some of us have been working on it for a few days help! Prove that the largest area of any quadrilateral is obtained when opposite angles are supplementary. Wow, what a classic and
3. ### Trignometry

If two angles are supplementary, then their sines are equal. Explain why. What about the cosines of supplementary angles? If you are not sure, calculate some examples.
4. ### geometery

does a rhombus has opposite angles that are supplementary yep they do..a rhombus' angles are all equivalent..so 360/4angles= 90 degrees each so if you add 90 and 90 = 180 and thus suplementary (180 deg) What do you mean by
5. ### geometry

a tree on a 30degree slope grows straight up .what are the measure of the greatest and smallest angles the tree make with the hill? you discovered that if a pair of angle is a linear pair ,the the angles are supplementary. does
6. ### Math

Find the measures of two supplementary angles if the difference of their measures is 56 degrees I know supplementary angles are the sum of the measure if two angles is 180 degrees but then what is the question asking?
7. ### Math

Complete the 2 column proof. Given m<rst = 5x and m<uvw = 7x <rstand <uvw are supplementary. Prove x=15 m<rst=5x and m<uvw=7x <rst and <uvw are supplementary given m<rst + <uvw = 180 definition of
8. ### Math

So my teacher marked this 0/6 but only told me to correct 2 things. Can some one check over this? If I'm right I need to email my teacher.. Complete the two column proof. Given: <2 and <5 are supplementary. Prove: L || M
9. ### geometry

If Quadrilateral QRST is a parallelogram, which is not necessarily true? a. Opposite angles are congruent. b. The diagonals bisect each other. c. Angles are four right angles. d. Consecutive angles are supplementary.
10. ### Geometry

Why do complementary and supplementary angles not have to be adjacent? As long as the two angles equal 90 degree then they will be complementary. As far as supplementary, as long as the two angle sum equals 180 degrees then they

More Similar Questions