Question

The terminal side of an angle theta in standard position coincides with the line y=1/2x in quadrant I. find sin theta to the nearest thousandth.

Answer 1

is this
\[y= \frac{1}{2}x \]

Answer 2

Yes.

Answer 3

I would pick a nice number for x (2 comes to mind) and plot the (x,y) pair
now we have the same problem as the others

Answer 4

notice that they say quadrant I

(because the line extends into quadrant III , they have to tell us which way to go on the line)

Answer 5

ok so.

Answer 6

yes, except it is hard to read (it looks like it's in code)

Answer 7

So then it would 1/1/sqrt(5) so because it wants it in decimal form the answer would be .444?

Answer 8

lol!

Answer 9

how did you get 0.444?

Answer 10

sorry I meant .447.

Answer 11

sin A = 1/sqrt(5)
(not 1/1/sqrt(5) )
but you must know that because you got 0.447 which is correct

Answer 12

oh.. I did 1/1/sqrt(5) and then switched it to 1/sqrt(5) because of the reciprical of 1/sqrt(5).

Answer 13

Does what I did make sense or did I do something and just happen to get the correct answer?

Answer 14

first, you should use the idea that a reciprocal is the number flipped. (Less chance of making a mistake)

second, in this problem they want the sin A so just use the definition of sin A
sin A= opp/hyp = 1/sqrt(5)
no flip involved

Answer 15

Oh. I guess I was still using csc. So I thought that it was 1/sin A and I did the reciprocal but I am not sure why.. Now that you explained that.

Answer 16

Ok. Thank you so much!

Answer 17

I assume you now know that
1/1/sqrt(5) and then switched it to 1/sqrt(5) is not correct

1/1/sqrt(5) is sqrt(5)

If you wanted the csc A and you know sin A= 1/sqrt(5) then flip to get sqrt(5)/1= sqrt(5)

Answer 18

Yes. Now I understand what I did wrong even though I happened upon the correct answer.