Question

I am working on averaqe rate of change of a function and i need help simplifying this
[sin 3pi/2 -sin5pi/6] / 3pi/2 -5pi/6

Answer 1

\[\Large{\sin(\frac{3\pi}2)-\sin(\frac{5\pi}2)\over\frac{3\pi}2-\frac{5\pi}2}\]

Answer 2

right?

Answer 3

yes

Answer 4

I would evaluate sine functions first.

Answer 5

wasn't that a 5pi/6?

Answer 6

oh yeah. i missed that. thanks

Answer 7

its 5pi/6

Answer 8

k... what do you get for sin(3pi/2) and sin(5pi/2)?

Answer 9

You can use unit circle, reference triangles, or even a calculator in radian mode.

Answer 10

the choice of ansers given were not completely simplified and thats whats confusing. When i use a calcultor, it simplifies it to 88.

Answer 11

Oh, I was just talking about the sines for the calculator.

Answer 12

but the choice of answers are all in fractions with pi in them

Answer 13

sin(3pi/2)=-1 What is sin(5pi/2)?

Answer 14

1

Answer 15

Yes, so you have -1-1 in the numerator... which simplifies to?

Answer 16

-2

Answer 17

Yes, now find the lowest common denominator of the fractions in the denominator.

Answer 18

Both 2 and 6 go into what number?

Answer 19

6

Answer 20

Yes, so change 3pi/2 into sixths by multiplying top and bottom by the number that makes 2 into 6...which is 3.

Answer 21

\[\frac{3}{3}\frac{3\pi}{2}=\frac{9\pi}{6}\]

Answer 22

9pi/6

Answer 23

ok

Answer 24

yes, now combine the fractions below by subtracting their numberators.

Answer 25

15pi/18

Answer 26

-6pi

Answer 27

\[\frac{9\pi}{6}-\frac{5\pi}{6}=\frac{4\pi}{6}\]

Answer 28

Here is what I have all together now.\[\frac{-2}{\frac{4\pi}{6}}\]

Answer 29

To divide fraction, invert the denominator and multiply by the numerator.\[-2(\frac{6}{4\pi})\]and reduce.

Answer 30

Any questions, or maybe a possible answer?

Answer 31

when you multipied the denom and numer of the first fraction by 3, why didnt you do it to the second fraction?

Answer 32

I was changing its form so that I could subtract the fractions. A common denominator is required to subtract fractions. By multiplying the same number top and bottom 3/3, it was like multiplying by one. It changes its form without changing its value.

Answer 33

ok i got it. because 9pi/6 is the same as 3pi/2

Answer 34

yes

Answer 35

and at that point it is compatable with 5pi/6... so we can subtract them.

Answer 36

ok. their final answer came out to be -9/4pi

Answer 37

bummer, that is not what I got... let me double check.

Answer 38

Oh I see... I missed that your original sine was 5pi/6 as well. I thought it was 5pi/2.

Answer 39

oh yeah, your right

Answer 40

sin(5pi/6)=1/2

Answer 41

-1-1/2 in the numerator gives -3/2

Answer 42

\[\frac{-\frac{3}{2}}\frac{4pi}{6}\]

Answer 43

editor is giving me problems...
-3/2 in the numerator
4pi/6 in the denominator

Answer 44

Invert and multiply denominator...\[-\frac{3}{2}\frac{6}{4\pi}\]

Answer 45

Bummer, it still looks bad on my screen. But yes, in the end it comes down to -9/4pi.

Answer 46

yes it sure does
. thanks a lot

Answer 47

No problem. It was fun until I started getting glitches.

Answer 48

lol. i know. its difficult typing those characters in

Answer 49

i got another similar problem