Question

Factor the algebraic expression below in terms of a single trigonometric function.

sin 2x + sin x - 2

Answer 1

@jim_thompson5910 Can you help me understand these?

Answer 2

sin(2x) = 2sin(x)cos(x)

Answer 3

Is the last term sin(x-2), or sin(x)-2?

Answer 4

sin ^2x + sin x - 2 I think it means sin(x). It just has a space there.

Answer 5

hint: let z = sin(x)

Answer 6

z^2 = sin^2(x)

Answer 7

so,

sin^2(x) + sin(x) - 2

turns into

z^2 + z - 2

Answer 8

hopefully you see how to go from here

Answer 9

(sin(x)+2)(sin(x)-1)? @jim_thompson5910

Answer 10

you nailed it

Answer 11

Awesome! I've got a few more I don't quite understand..

Answer 12

ok I'll help with 2 more

Answer 13

Find sin θ if cot θ = - 4 and cos θ < 0. This one is like the one we did earlier, but a little different. I have no idea what it is asking for.

Answer 14

what is cot in terms of opp, adj, hyp?

Answer 15

adj/opp

Answer 16

so

cot(theta) = -4 and cot(theta) = adj/opp

because -4 = -4/1, we know that

adj = -4
opp = 1

Answer 17

Now draw a right triangle with that info and use it to find the hypotenuse

Answer 18

sqrt17

Answer 19

good

Answer 20

now you can find sin(theta)

Answer 21

sqrt17/17?

Answer 22

correct

Answer 23

Awesome. Hang on. I working the next one.

Answer 24

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