Question

Simplify: (sin Θ − cos Θ) − (sin Θ + cos Θ)^2

Answer 1

@phi

Answer 2

I would recommend expanding the squared term first.

Answer 3

can you multiply (sin x + cos x)(sin x + cos x) ?

Answer 4

Well its subtraction not multiplication

Answer 5

you have
(sin Θ + cos Θ)^2

the 2 means "square" i..e multiply by itself.

Answer 6

oh well i guess you could

Answer 7

btw, I'm not getting anything pretty out of this. Do you have choices ?
("simplification" is sometimes subjective)

Answer 8

−sin2 Θ
−cos2 Θ
0
−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Answer 9

they have a peculiar notion of "simple"

any way, can you multiply out
(sin x + cos x)(sin x + cos x) ?

Answer 10

some people use FOIL (first, outer, inner, last) to remember how

Answer 11

@agent0smith remember when we solved this question for a different user a while back? x'D

Answer 12

1+sin2x

Answer 13

you (or your program) went too far.

Answer 14

what are you looking for ?

Answer 15

1+2 cos x sin x

Answer 16

sin2x is also 2sin x cos x
(and none of your answers changed the 2 sin x cos x to sin 2x)

Answer 17

now you have
sin x - cos x - (1+ 2 sin x cos x)

which only matches one of your choices.

Answer 18

i don't get it still

Answer 19

you start with
sin x - cos x - ( sin x + cos x)^2
you "square" the last expression, and get
sin x - cos x - (1+ 2 sin x cos x)
now "distribute" the - sign in the last term: multiply each term by -1

Answer 20

Okay but how does that lead you to one of the answers like maybe I'm not seeing it idk

Answer 21

did you distribute the -1 ? what did you get ?

Answer 22

sin x - cos x - 1 - 2 sin x - cos x

Answer 23

there is only one choice that has that many terms. If you re-order the terms, do you get a match ?

Answer 24

Ahhhh d

Answer 25

though we have to tweak your expression
sin x - cos x - 1 - 2 sin x - cos x

should be
sin x - cos x - 1 - 2 sin x cos x

Answer 26

correct me if I'm wrong but shouldn't the amplitude of this be 4 ?

Answer 27

I still think it's ugly. but choice D is the answer.

Answer 28

a "normal" sin curve sin(x)
goes between -1 and +1
the amplitude is the "number" out front, multiplying the sin(x)
e.g. 1*sin(x)

in other words, the amplitude is from the "mid-point" to the top
or , if you like, 1/2 of the full travel from bottom to top.

Answer 29

the "mid-line" is the line half-way between the top and bottom. (definitely not y=1 in your picture)

Answer 30

gotcha so 2