Trigonometric Functions and Unit Circle

The video tutorial by Mr. Tarrou revisits the unit circle and explains how to evaluate basic trigonometric functions without a calculator. It covers the importance of keeping answers in exact form, the properties of sine, cosine, and tangent, and introduces inverse and reciprocal trig functions. The tutorial emphasizes understanding the unit circle and the significance of even and odd functions, as well as handling undefined values in trig functions.

Why is it important to keep trigonometric values in exact form?

• To avoid using decimals

• To make calculations easier

• To ensure precision and understanding

• To avoid using calculators

How many basic angles are used in the unit circle?

• 8

• 16

• 12

• 20

Which triangles are used to form the unit circle?

• 30-30-120 and 60-60-60

• 30-60-90 and 60-60-60

• 30-60-90 and 45-45-90

• 45-45-90 and 60-60-60

What is the sine of an angle in the unit circle?

• y over r

• x over r

• x over y

• y over x

What is the cosine of pi/3 in the unit circle?

• sqrt(3)/2

• 1

• 0

• 1/2

What is a coterminal angle?

• An angle that is a multiple of 90 degrees

• An angle that is a multiple of 180 degrees

• An angle that shares the same terminal side

• An angle that is a multiple of 360 degrees

What is the sine of negative pi/3?

• 1/2

• -sqrt(3)/2

• -1/2

• sqrt(3)/2

What is an even function in trigonometry?

• A function where f(x) = x

• A function where f(-x) = -f(x)

• A function where f(-x) = f(x)

• A function where f(x) = 0

What is the tangent of 4pi/3?

• -sqrt(3)

• 1

• -1

• sqrt(3)

Why can some trigonometric functions be undefined?

• Because they are not real numbers

• Because they are not on the unit circle

• Because they have a negative value

• Because they have a zero in the denominator