Question

factor the algebraic expression below in terms of a single trigonometric function help?


sin^2x+sinx-2

Answer 1

sin(x) -2, or sin(x-2)?

Answer 2

no its (sin^2)x + sin(x) -2 kinda if you look at it like that

Answer 3

@jdoe0001

Answer 4

ok.... take a peek at the expression
\(\bf sin^2(x)+sin(x)-2\\
\text{let's make sin(x) = a}\\
a^2+a-2\\
\text{now you have a quadratic function}\)

Answer 5

so now If I solve for "a" that will be my answer?
@jdoe0001

Answer 6

so you need 2 numbers, factors of "2"
added together should give 1, for 1a middle term
multiplied together should give -2, for -2 the constant

yes

Answer 7

so would my answer be....sin^3-2?
@jdoe0001

Answer 8

ahemm... no :/
on a quadratic usually you'd factor it to 2 binomials

2 factors of 2 that add to 1 and multiply to -2
let's see

+2 * -1 = -2
+2 +(-1) = 1

low and behol!
so your binomials will be (a + 2)(a - 1)
now if we change the "a" back to sin(x)

\(\bf ( sin(x) +2 ) ( sin(x) - 1)\)

Answer 9

oh ok great haha, @jdoe0001 , so then multiply and I have my answer?

Answer 10

well, no multiplication for this instance, all they want is
\(\bf \text{ in terms of a single trigonometric function }\)

Answer 11

that's just in form of sin(x)-2 ? @jdoe0001

Answer 12

oh no then I would just leave it in the form you gave me ?

Answer 13

yes, just leave in the forms of the 2 binomial factors, since is all that's being required :)

Answer 14

super, thank you so much sorry I was trying to refigure this out, but anyhow thanks a billon!!! @jdoe0001

Answer 15

yw