sine of theta

[drsearllie]

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin of theta?

I can't seem to think this one through. I've been dealing with 30, 60, 90 special triangles but I don't think this is one. If not a special triangle, then I'm not sure how to proceed because it seems like I need atleast one leg length or an angle Rioto get anywhere.

 

[Deleted member 4993]

(This may be a duplicate post. Sorry)
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin of theta?

I can't think this one out. This doesn't seem to be a special triangle like I've been dealing with.

Start with:

Draw the circle, with a center at O.

Choose a point P

Drop a perpendicular from P to the x-axis. The point where this perpendicular touches the x-axis, call it P_x.

Drop a perpendicular from P to the x-axis. The point where this perpendicular touches the y-axis, call it P_y.

Now continue following given directions in your problem.....

 

[drsearllie]

Yeah, that doesn't seem to solve the problem. The ordered pair would be (I think anyway), (x,2x) where x is unknown length, making sin (2x).

 

[Deleted member 4993]

Yeah, that doesn't seem to solve the problem. The ordered pair would be (I think anyway), (x,2x) where x is unknown length, making sin (2x).

Well - it does..

What is tan(Θ) = 2

What is the hypotenuse of that triangle?

What is sin(Θ)?

 

[stapel]

Yeah, that doesn't seem to solve the problem.

Really? When you drew the figure, labelled the two sides appropriately, used the Pythagorean Theorem to label the hypotenuse, and applied the sine-ratio definition, this got you no closer to the answer of what the value of the sine is?

Then please write back explaining what you got when you followed the provided steps. Thank you!

 

[drsearllie]

This was in a multiple choice test and those aren't the answers. The right answer supposedly is 2sqrt(0.2). I don't understand how they got this answer. Especially when they do not give any values except the implied hypotenuse of 1. This does not produce a special triangle like the lesson teaches.

 

[stapel]

This was in a multiple choice test and those aren't the answers.

We provided you with step-by-step instructions. Are you saying that the actual question really asked for the method of solution, rather than a value, so the "answers" were various methodologies?

The right answer supposedly is 2sqrt(0.2). I don't understand how they got this answer.

Try actually doing the steps you've been given:

Draw the picture. Label the sides. Apply the Pythagorean Theorem to create an equation. Solve that equation. Plug that solution value back into the picture. Apply the sine ratio. What do you get?

Please do the steps, and then reply showing your steps and your results, clearly pointing out how these steps did not lead to the answer. Thank you.