Question

point P = (x, - 3/7}) lies on the unit circle shown below. What is the value of x in simplest form?

Answer 1

Answer:

± 2√10/7

Step-by-step explanation:

Equation of the circle:

• x² + y² = r² where x and y are coordinates and r is the radius.

We assume that the centre of the circle is on the coordinates (0,0). So in such a case, the radius always equals 1.

• x²+y² = 1

Point P = (x,-3/7) = (x,y)

This gives y = -3/7

So

• x²+(-3/7)² = 1
• x² + 3²/7² = 1
• x² + 9/49 = 1

Subtract 9/49 from both sides:

• x² = 1-9/49 = 49-9/49 = 40/49

Taking square root on both sides:

• x = √40/√49 = ± 2√10/7