Evaluate the six trigonometric functions of the real numbers

The video tutorial explains how to evaluate the six trigonometric functions for a given real number using the unit circle. It covers the significance of negative angles, locating points on the unit circle, and calculating sine, cosine, tangent, cosecant, secant, and cotangent. The tutorial emphasizes the importance of simplifying fractions and avoiding radicals in denominators.

What does a negative angle indicate when using the unit circle?

• A change in angle size

• A clockwise direction

• A change in radius

• A counterclockwise direction

What is the y-coordinate for the angle -4π/3 on the unit circle?

• sqrt(3)/2

• -1/2

• -sqrt(3)/2

• 1/2

How is the tangent of an angle calculated using its coordinates?

• y/x

• x-y

• x/y

• x+y

What is the cosecant of an angle if its sine is sqrt(3)/2?

• sqrt(3)/2

• 1/sqrt(3)

• 2

• 2/sqrt(3)

What must be done if a trigonometric expression has a radical in the denominator?

• Multiply by the radical over itself

• Multiply by the reciprocal

• Add a constant

• Divide by the radical

What is the secant of an angle if its cosine is -1/2?

• sqrt(3)/2

• -sqrt(3)/2

• 2

• -2

What is a key rule when simplifying trigonometric expressions?

• Always have a fraction in the denominator

• Always have a radical in the denominator

• Never have a radical in the numerator

• Never have a fraction or radical in the denominator