Understanding the Unit Circle and Trigonometric Functions

The video tutorial reviews the SOHCAHTOA acronym and its application on the unit circle, explaining how sine, cosine, and tangent relate to the x and y coordinates. It explores the symmetry of the unit circle and how to reflect triangles across axes. The tutorial also covers radian units, showing how to convert between radians and degrees, and provides examples of calculating trigonometric ratios for common angles using the unit circle.

What is the sine of an angle in the unit circle if the opposite side is 1/2 and the hypotenuse is 1?

• 0

• Square root of 3 over 2

• 1/2

• 1

In which quadrant is the x-coordinate negative and the y-coordinate positive?

• First Quadrant

• Second Quadrant

• Third Quadrant

• Fourth Quadrant

How many degrees are equivalent to pi radians?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

What is the cosine of 5 pi over 4?

• Square root of 2 over 2

• 1/2

• -1/2

• -Square root of 2 over 2

Which acronym helps remember the sign of trigonometric functions in different quadrants?

• Pythagorean

• SOHCAHTOA

• ASTC

• Sine Rule

What is the tangent of 2 pi over 3?

• Square root of 3

• -Square root of 3

• 1

• -1

If an angle is in the 60-degree family, what is its reference angle in radians?

• Pi

• Pi over 3

• Pi over 4

• Pi over 6

What is the cosine of 5 pi over 3?

• 1/2

• -1/2

• Square root of 3 over 2

• -Square root of 3 over 2

Which leg is shorter in a 60-degree triangle on the unit circle?

• None

• Adjacent

• Opposite

• Hypotenuse

What is the value of sine for a 45-degree angle on the unit circle?

• Square root of 2 over 2

• 0

• Square root of 3 over 2

• 1