Question

If the point (x,square root 3/3) is on the unit circle, what. is x?

A) 2/3
B) square root(6)/3
C) 4/9
D) square root(2)/3

Answer 1

The x-value for the point (x, square root of 3/3) on the unit circle is found using the Pythagorean theorem. Substituting the y-value and solving for x, we get x = square root of 6/3. Therefore, the answer is B) square root of 6/3.

Step-by-step explanation:

If the point (x, square root of 3/3) is on the unit circle, we can find x by using the Pythagorean theorem, which in the context of the unit circle is given by x² + y² = 1. Since we know y = square root of 3/3, we can substitute this value into the equation to find x:

x² + (square root of 3/3)² = 1

x² + 3/9 = 1

x² + 1/3 = 1

x² = 1 - 1/3

x² = 2/3

x = square root of (2/3)

To express x as a radical fraction, we find the square root of the numerator and the denominator separately:

x = square root of 2 / square root of 3

x = square root of 2/3

By rationalizing the denominator, we get:

x = (square root of 2/3) * (square root of 3/square root of 3)

x = square root of 6/3

x = square root of 6/3

Therefore, the correct answer is B) square root of 6/3.

Answer 2

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