Question

What is the y-value for f(x) = cos(x) when x = -90°?

Answer 1

There is an identity `cos(-A)=cos(A)`. First, apply this rule.

Answer 2

ok

Answer 3

I mean, first plug in -90 for x, into cos(x).

Answer 4

and then apply that

Answer 5

sorry im like also taking notes cuz i dont really get this

Answer 6

so itll be positive 90 right?

Answer 7

your problem is:
\(\large\color{black}{ \displaystyle f(x)= {\rm Cos}(x) }\)

plug in -90 for x,
\(\large\color{black}{ \displaystyle f(-90)= {\rm Cos}(-90) }\)

then since we know that `cos(-a)=cos(a)`, we get:
\(\large\color{black}{ \displaystyle f(-90)= {\rm Cos}(90) }\)

Answer 8

Do you know what \(\large\color{black}{ \displaystyle {\rm Cos}(90) }\) is ?

Answer 9

wait wait hold on

Answer 10

sure, take your time.

Answer 11

is it -0.44?

Answer 12

i think im wrong

Answer 13

yes, \(\large\color{black}{ \displaystyle {\rm Cos}(90) }\) is not -0.44

Answer 14

try again please.

Answer 15

mmmm 51

Answer 16

no wait

Answer 17

no idk wats cos (90) ....im so sorry i really am trying :(

Answer 18

\(\large\color{black}{ \displaystyle {\rm Cos}(90)=1 }\)

Answer 19

why

Answer 20

that is a good question.
\(\large\color{black}{ \displaystyle {\rm Cos}(90)={\rm Cos}(45+45) ={\rm Cos}(45) {\rm Cos}(45) -{\rm Sin}(45) {\rm Sin}(45) }\)
\(\large\color{slate}{ \\[0.5em] }\)
`sine = opposite / hypotenuse`
`cosine = adjacent / hypotenuse`\(\large\color{slate}{ \\[0.8em] }\)
since opposite and adjacent sides are formed \(\large\color{slate}{ \\[0.8em] }\)
by the same angle, they are (themselves) the same.\(\large\color{slate}{ \\[0.8em] }\)
Saying that `opposite=adjacent`\(\large\color{slate}{ \\[0.8em] }\)
And if `opposite=adjacent`, \(\large\color{slate}{ \\[0.8em] }\)
then `opposite / hypotenuse = adjacent / hypotenuse` \(\large\color{slate}{ \\[0.8em] }\)
which is essentially telling us that `sin(45)=cos(45)`, \(\large\color{slate}{ \\[0.8em] }\)
because `sine = opposite / hypotenuse` and `cosine = adjacent / hypotenuse`

Then continuing on our math,
\(\large\color{black}{ \displaystyle {\rm Cos}(90)={\rm Cos}(45+45) ={\rm Cos}(45) {\rm Cos}(45) -{\rm Sin}(45) {\rm Sin}(45) }\)

if `sin(45)=cos(45)` , then `sin(45)sin(45)=cos(45)cos(45)`

and therefore,
\(\large\color{black}{ \displaystyle {\rm Cos}(45) {\rm Cos}(45) -{\rm Sin}(45) {\rm Sin}(45)\color{blue}{=0} }\)