Trigonometric Functions and Unit Circle

The video tutorial explains how to find exact trigonometric function values using the unit circle. It covers sketching angles in standard position and determining where the terminal side intersects the unit circle to find cosine and sine values. The tutorial demonstrates finding the sine of 3π/4 and the cosine of -11π/4, using methods like dividing the circle into equal parts and employing coterminal angles. It emphasizes the utility of these techniques when angles are not labeled on the unit circle.

What is the primary benefit of using the unit circle to find trigonometric function values?

• It only works for angles in the first quadrant.

• It eliminates the need for a calculator.

• It provides exact values for sine and cosine.

• It simplifies complex numbers.

What is the significance of the terminal side in trigonometry?

• It is used only for sine calculations

• It is always on the x-axis

• It provides the exact trigonometric values

• It determines the quadrant of the angle

When sketching 3π/4 radians on the unit circle, what is the y-coordinate of the intersection point?

• Negative square root of 2 divided by 2

• Square root of 2 divided by 2

• 0

• 1

What is the x-coordinate of the intersection point for 3π/4 radians on the unit circle?

• Square root of 2 divided by 2

• 0

• Negative square root of 2 divided by 2

• 1

How can you find the terminal side of an angle that is a multiple of π/4 radians?

• By dividing the circle into 3 equal parts

• By counting in increments of π/4 radians

• By rotating clockwise only

• By using a calculator

Why is it helpful to divide the unit circle into increments of π/4 radians?

• To simplify the calculation of tangent

• To avoid using negative angles

• To easily count and locate angles

• To find angles in the third quadrant

What is the cosine value for the angle -11π/4 radians?

• Square root of 2 divided by 2

• Negative square root of 2 divided by 2

• 1

• 0

What is a coterminal angle?

• An angle that is a multiple of π

• An angle that is always negative

• An angle that shares the same terminal side

• An angle that is always positive

How can you find a coterminal angle for -11π/4 radians?

• By adding multiples of 2π

• By subtracting multiples of π

• By dividing by 2

• By adding multiples of π/2

What happens when you add 2π to an angle?

• The angle becomes negative

• The angle doubles

• The angle remains unchanged

• The angle becomes coterminal with the original