Understanding Periodic Properties of Trigonometric Functions

The video tutorial explains the periodic properties of trigonometric functions, focusing on sine and cosine. It demonstrates how adding or subtracting full rotations (360 degrees or 2π) results in coterminal angles with the same trigonometric values. The tutorial includes examples to illustrate these concepts, such as evaluating sine of 420 and 750 degrees, and cosine of negative 2π/3, using the unit circle and reference angles.

What is the value of sine when you add 360 degrees to an angle?

• It becomes zero

• It becomes negative

• It remains the same

• It doubles

Which of the following trigonometric functions also exhibit periodic properties like sine?

• Cosine

• All of the above

• Tangent

• Cotangent

What is the sine of 420 degrees equivalent to?

• Sine of 120 degrees

• Sine of 30 degrees

• Sine of 60 degrees

• Sine of 90 degrees

How do you find a coterminal angle for a given angle?

• Multiply by 2

• Add or subtract 180 degrees

• Divide by 2

• Add or subtract 360 degrees

What is the cosine of negative 2π/3 equivalent to?

• Cosine of π/3

• Cosine of 4π/3

• Cosine of 2π

• Cosine of π

What is the reference angle for 4π/3?

• π/2

• π/3

• π/4

• π/6

What is the x-value of the cosine function at 4π/3?

• √3/2

• -√3/2

• -1/2

• 1/2

What is the sine of 750 degrees equivalent to?

• Sine of 120 degrees

• Sine of 30 degrees

• Sine of 90 degrees

• Sine of 60 degrees

How many times do you need to subtract 360 from 750 to find an equivalent angle?

• Once

• Twice

• Three times

• Four times

What is the value of sine at 30 degrees?

• 1

• 0

• 1/2

• √3/2