Why the unit circle is so helpful for us to evaluate trig functions

The video tutorial covers the significance of the unit circle in trigonometry, focusing on special triangles like 30-60-90 and 45-45-90. It explains how to convert angles to radians and highlights the importance of memorizing key points on the unit circle. The tutorial also demonstrates how the unit circle simplifies finding sine values for angles like 90 and 180 degrees, which cannot be evaluated using triangles alone.

Why is the unit circle useful in trigonometry?

• It provides a visual representation of angles.

• It simplifies the evaluation of sine, cosine, and tangent.

• It helps in solving algebraic equations.

• It is used to measure angles in degrees.

What is the radian measure for a 30-degree angle?

• π/4

• π/2

• π/6

• π/3

Which of the following is a coordinate point for a 45-degree angle on the unit circle?

• (1/2, √3/2)

• (√2/2, √2/2)

• (0, 1)

• (1, 0)

Why does the teacher emphasize memorizing only three points on the unit circle?

• Because the unit circle is not used in exams.

• Because the rest are not important.

• To simplify learning and focus on key concepts.

• To avoid confusion with other subjects.

What is the sine of 90 degrees according to the unit circle?

• 0

• 1

• -1

• Undefined

Why can't a triangle be used to find the sine of 180 degrees?

• Because 180 degrees is not a valid angle in a triangle.

• Because it is a negative angle.

• Because it requires a special type of triangle.

• Because it is outside the range of the unit circle.

What is the Y-coordinate of the point on the unit circle at 180 degrees?

• -1

• 0

• Undefined

• 1