Understanding Quadrants and Unit Circle

The video tutorial explains how to find the x-coordinate of a point on the unit circle given its y-coordinate and quadrant. It covers the properties of the unit circle, the equation of a circle, and solving for x using substitution and a reference triangle. The tutorial also demonstrates calculating the x-coordinate and provides a decimal approximation, emphasizing the importance of using exact values unless instructed otherwise.

In which quadrant is the point P located if its y-coordinate is -2/3?

• 4th Quadrant

• 3rd Quadrant

• 2nd Quadrant

• 1st Quadrant

What is the radius of the unit circle?

• 0

• 3

• 1

• 2

What is the equation of the unit circle?

• x^2 + y^2 = 2

• x^2 + y^2 = 0

• x^2 + y^2 = 1

• x^2 + y^2 = 3

What value is substituted for y in the unit circle equation to solve for x?

• 1/3

• -1/3

• 2/3

• -2/3

Which theorem is used to find the x-coordinate using a reference triangle?

• Remainder Theorem

• Fundamental Theorem of Calculus

• Binomial Theorem

• Pythagorean Theorem

What is the x-coordinate of the point P in the 4th quadrant?

• Square root of 5 divided by 3

• Square root of 5 divided by 5

• Square root of 5 divided by 2

• Square root of 5 divided by 4

Why do we only consider the positive solution for x in the 4th quadrant?

• Because y-coordinates are positive in the 4th quadrant

• Because x-coordinates are positive in the 4th quadrant

• Because x-coordinates are negative in the 4th quadrant

• Because y-coordinates are negative in the 4th quadrant

What is the decimal approximation of the x-coordinate rounded to three decimal places?

• 0.765

• 0.755

• 0.775

• 0.745

What should you do if not specifically asked to round the x-coordinate?

• Round to the nearest whole number

• Do not round

• Always round to three decimal places

• Always round to two decimal places

What is the importance of obtaining a common denominator when solving for x?

• It changes the value of x

• It is not necessary

• It makes the equation more complex

• It simplifies the equation