Question

Please help me answer this:

Determine whether each of the following points lie in the unit circle.
1. (3/5, 4/5)
2. (0.8, -0.6)
3. (2 2/3, -1/3)
4. (2, -1)
5. (-8/17, -15/17)

Thank you!

Answer 1

cos (theta) = x/r. The radius of the unit circle is 1. That gives cos(theta) = x.
Likewise, on the unit circle sin(theta) = y.

Also, recall that sin^2 (theta) + cos^2(theta) = 1.

For 1. (3/5, 4/5)

Does (3/5)^2 + (4/5)^2 = 1 ? If yes, the point is on the unit circle. If no, then the point is not on the unit circle.

Answer 2

Note: Recall that the maximum and minimum values of the cosine and sine functions are 1 and -1, respectively. @dsrl26

Answer 3

Need to c drawing @directrix

Answer 4

I don't see that a drawing would help on this problem if a person knows trig properties. In general, I agree that the role of diagrams in mathematics cannot be overstated.
@shamim

Answer 5

Thank you for you for helping me. I really find it hard. @Directrix @shamim

Answer 6

Did you get an answer for this: (3/5)^2 + (4/5)^2 ?
Don't give up just yet. @dsrl26

Answer 7

I will try to solve it. @Directrix

Answer 8

Multiply 3/5 times 3/5.
Multiply 4/5 times 4/5.
Add what you get for each computation together.

Answer 9

Oh, I got it! Thank you so much! @Directrix

Answer 10

What did you get?

Do the same here:

2. (0.8, -0.6)

Does .8 ^2 + (-.06)^2 = 1?

Answer 11

Yes. Only numbers 3 and 4 do not lie on the unit circle. Thank you so much, Sir!

Answer 12

My answer for number 1 is 25/25 or 1. @Directrix

Answer 13

Correct. So, so far the points on #1 and #2 are on the unit circle.

Look at #3 3. (2 2/3, -1/3) The x value of 2 and 2/3 cannot be the x coordinate of a point that lies on the unit circle because the radius of the unit circle is 1.

When you square 2 2/3 and add it to the square of -1/3, you will exceed 1.So, that point cannot be on the unit circle.

Answer 14

Now, it's your turn to decide if this point is on the unit circle.

4. (2, -1)

@dsrl26