Finding Trigonometric Coordinates for the 45-Degree Angle on the Unit Circle

This lesson teaches how to find the trigonometric coordinates for a 45-degree angle on the unit circle using properties of isosceles right triangles. It covers the application of the Pythagorean theorem to determine the length of the triangle's legs and explains the process of rationalizing the denominator to simplify expressions. The lesson concludes with determining the coordinates as the square root of 2 over 2 for both sine and cosine of the 45-degree angle.

What is the significance of the hypotenuse in an isosceles right triangle placed on the unit circle?

• It is always greater than 1.

• It is equal to the radius of the circle.

• It represents the diameter of the circle.

• It is irrelevant to the unit circle.

How do you determine the length of the legs in an isosceles right triangle on the unit circle?

• By using the cosine rule.

• By applying the Pythagorean theorem.

• By using the sine rule.

• By measuring directly.

What is the result of simplifying x squared equals 1/2?

• x equals 2

• x equals 1 over the square root of 2

• x equals 1/2

• x equals 1

Why is it necessary to rationalize the denominator when finding the trigonometric coordinates?

• To increase the accuracy of the result.

• To avoid leaving a radical in the denominator.

• To simplify the numerator.

• To make calculations easier.

What are the trigonometric coordinates for the 45-degree angle on the unit circle?

• (1/2, 1/2)

• (1, 0)

• (0, 1)

• (√2/2, √2/2)