Question

What is the simplified form of sin(x + p)?
a. cos x b. sin x c. –sin x d. –cos x

Answer 1

Assuming p = period of the function or 2pi, sin(x+p) = sin(x).

Thus, answer B, or sinx, would be the correct answer.

Answer 2

alright but how would I get that

Answer 3

I gather he meant to say "pi", for \(\large \pi \)

Answer 4

ohhhh okay thanks man/women.

Answer 5

so, use the sum trig identity -> http://www.sosmath.com/trig/addform/img1.gif for sine

Answer 6

and see what you get

Answer 7

but how would I know what to do if the only information there is sin(x+p)

Answer 8

well, off the trig identities there, which one do you think we could use?

Answer 9

i am terribly sorry but i am in james Madison high school from ashworth

Answer 10

you're sorry you're at that HS.... or you're sorry for James Madison who's been dead for about 190 years?

Answer 11

sorry for being at this high school the teachers don't really teach any thing.
but you would use the sin(a+b)

Answer 12

right, as you can see in the picture, the identity is sin(a + b) = sin(a)cos(b)+cos(a)sin(b)
thus \(\bf sin(x+\pi)\\\quad \\ \quad \\

sin(x+\pi) \implies sin(x)cos(\pi)+cos(x)sin(\pi)\\
\quad \\\quad \\
\textit{what's the }sin(\pi) \textit{ and the } cos(\pi)\quad ?\)

Answer 13

if you check your Unit Circle, you'll see what those two are

Answer 14

what unit circle?

Answer 15

hehh, man, that'.s... anyhow... if you need a Unit Circle, as you should have had one, many online, try this one --> http://i.stack.imgur.com/r8uHr.gif

Answer 16

so.. \(\bf \textit{what's the }sin(\pi) \textit{ and the } cos(\pi)\quad ?\)

Answer 17

dude i am totally lost by looking at this but i would have to guess it is 180 for both?

Answer 18

heheh, that Unit Circle, or any good unit circle, will have the degrees, 180 yes, as well as the Radians units, notice it shows as \(\large 180^o = \pi\)

Answer 19

yes. i do

Answer 20

so would you plug 180 into sin(pi) and cos(pi)

Answer 21

yeap

Answer 22

alright so i got -1

Answer 23

-1? for...?

Answer 24

for sin and cos

Answer 25

hmm.... on the Unit Circle, there's a pair of values, just like (x, y) coordinates
the pair is (x, y) also or (cosine, sine) pair

so one value is for cosine, the other is for sine

Answer 26

if you notice the top-right-hand corner, it shows the (cos, sin) pair reference

Answer 27

oh oh okay now i see it so it would be (-1,0)

Answer 28

that means that \(\bf \large cos(\pi) = -1 \qquad sin(\pi) = 0\)

so replace that in \(\bf sin(x)cos(\pi)+cos(x)sin(\pi) \)
see what you get

Answer 29

so you would get sinx

Answer 30

\(\bf sin(x)cos(\pi)+cos(x)sin(\pi) \implies sin(x)-1+cos(x)0\\\quad \\
sin(x)-1+cos(x)0 \implies sin(x)-1+0 \implies -sin(x)\)

anything * 0 = 0

Answer 31

alright now this all makes sense

Answer 32

thanks man appreciate it

Answer 33

yw