Trigonometric Functions and Their Properties

The video tutorial explains how to simplify trigonometric expressions involving inverse trigonometric functions. It covers three main examples: simplifying sine of arcsine of -3/10, explaining why arccosine of 1.5 does not exist, and simplifying tangent of arctangent of 5.4. The tutorial discusses the domains and ranges of these functions and provides step-by-step simplifications.

What is the first step in simplifying the expression sine of arcsine of negative 3/10?

• Determine the domain of arcsine

• Find the cosine of the angle

• Calculate the tangent of the angle

• Evaluate the arcsine of negative 3/10

What is the range of the arcsine function?

• From negative PI to PI

• From 0 to 2PI

• From negative PI/2 to PI/2

• From 0 to PI

In which quadrant does the angle lie if the sine value is negative?

• Quadrant 1

• Quadrant 4

• Quadrant 2

• Quadrant 3

What is the simplified form of sine of arcsine of negative 3/10?

• 0

• 1

• Negative 3/10

• 3/10

Why does the expression cosine of arccosine of 1.5 not exist?

• 1.5 is greater than PI

• 1.5 is not a real number

• 1.5 is not in the domain of arccosine

• 1.5 is not in the range of cosine

What is the domain of the arccosine function?

• All real numbers

• From negative 1 to positive 1

• From 0 to PI

• From negative PI/2 to PI/2

What is the domain of the arctangent function?

• From negative PI/2 to PI/2

• All real numbers

• From 0 to PI

• From negative 1 to positive 1

What is the result of simplifying tangent of arctangent of 5.4?

• Does not exist

• 1

• 0

• 5.4

What is the range of the arctangent function?

• From negative PI/2 to PI/2

• From 0 to 2PI

• From negative PI to PI

• From 0 to PI

Which trigonometric function has a range from negative PI/2 to PI/2?

• Cosine

• Sine

• Cosecant

• Tangent