Trigonometric Functions and Angles

The video tutorial explains how to evaluate trigonometric expressions involving inverse trigonometric functions. It covers four main examples: cosine of inverse sine of sqrt(3)/2, sine of inverse cosine of 1/2, tangent of inverse cosine of sqrt(2)/2, and sine of inverse tangent of sqrt(3)/3. Each example involves identifying the corresponding angle on the unit circle, determining the quadrant, and simplifying the expression. The tutorial emphasizes understanding the relationships between trigonometric functions and their inverses, as well as the use of the unit circle to find angles and evaluate expressions.

What is the angle in radians for which the sine value is square root three divided by two?

• pi over 3

• pi over 2

• pi over 6

• pi over 4

What is the cosine of pi over three radians?

• 1

• 0

• square root 3/2

• 1/2

Which angle in radians has a cosine value of one half?

• pi over 2

• pi over 4

• pi over 3

• pi over 6

What is the sine of pi over three radians?

• 1/2

• 1

• square root 3/2

• square root 2/2

What is the angle in radians for which the cosine value is square root two divided by two?

• pi over 4

• pi over 2

• pi over 3

• pi over 6

What is the tangent of pi over four radians?

• 0

• 1

• square root 3

• 1/2

What is the angle in radians for which the tangent value is square root three divided by three?

• pi over 2

• pi over 4

• pi over 3

• pi over 6

What is the sine of pi over six radians?

• 1

• 1/2

• square root 3/2

• square root 2/2

How do you rationalize the expression square root three divided by three?

• Add square root 3

• Multiply by 3

• Divide by 3

• Multiply by square root 3

In which quadrant is the angle with a positive tangent value of square root three divided by three?

• Third

• Second

• Fourth

• First