Question

Find sin θ if cot θ = - 2 and cos θ < 0.

I need help I give medals
the options are

-1/2
-5
sqrt5/2
sqrt5/5

Answer 1

@rob1525 ?

Answer 2

Hey, I answered on the other question.

Answer 3

well -2 is not in the form of radians. I'm not sure yet.

Answer 4

@ivanmlerner so what is the answer to this one sorry I didnt put the options on that one ...ill give a medal though

Answer 5

No problem, I took some time to answer its ok. But I dont see my answer on your options. If you look at the picture I got 1/sqrt(5)

Answer 6

so this picture shows the cot theta = -2/1 now do the sin of the same angle. do you know what i mean?

Answer 7

Oooh I see now, 1/sqrt(5)=sqrt(5)/5 and thats one of the options

Answer 8

Actually the picture is wrong because 1 is positive so its actully in the 2 quadrant.

Answer 9

Nice way @rob1525.

Answer 10

@ivanmlerner can you help with :
Factor the algebraic expression below in terms of a single trigonometric function.

sin 2x + sin x - 2

Answer 11

Sure, do you know the trig identity for sin(2x)?
This question has something to do with that but it is just something extra, do you have a basic understanding of complex numbers?

Answer 12

is it 2sin(x)cos(x) @ivanmlerner

Answer 13

Yes, so you just need to use that, and the formula cos=sqrt(1-sin^2) to transform everything into sin

Answer 14

no sure how to though thats as far as i know ... can you run through it for me

Answer 15

not*

Answer 16

@ivanmlerner

Answer 17

Sure, you have\[\sin(2x)+\sin x-2\]Using the formula for sin(2x)\[2\sin x \cos x+\sin x-2\]What the problem wants is that you use only one trig function (sin or cos in this case) in the formula, so we need to get rid of the cos. and for that we use the formula sin^2+cos^2=1 and this formula can be rearanged to cos=sqrt(1-sin^2) so we need only to substitute now on the formula:\[2\sin x \cos x+\sin x-2=2\sin x \sqrt{1-\sin^2 x}+\sin x -2\]And I believe thats it because we only use sin(x) in this formula.

Answer 18

sqrt5/5