Understanding Inverse Trigonometric Functions

The video tutorial explains inverse trigonometric functions, focusing on arcsine and arctangent. It demonstrates how to calculate the arctangent of -1 using the unit circle and discusses the importance of restricting the range of inverse tangent functions to ensure a one-to-one mapping. The tutorial also covers the relationship between tangent and slope, using visual aids like the unit circle to enhance understanding.

What is another way to express the arcsine of x?

• Inverse cosine of x

• Inverse sine of x

• Inverse cotangent of x

• Inverse tangent of x

If someone asks for the inverse tangent of x, what are they essentially asking?

• What angle has a tangent of x?

• What angle has a sine of x?

• What angle has a cosine of x?

• What angle has a cotangent of x?

What is the relationship between tangent and the unit circle?

• Tangent is the slope of the line from the origin to a point on the unit circle.

• Tangent is the y-coordinate on the unit circle.

• Tangent is the x-coordinate on the unit circle.

• Tangent is the radius of the unit circle.

What is the arctangent of -1 in degrees?

• 45 degrees

• -45 degrees

• 90 degrees

• -90 degrees

How do you convert -45 degrees to radians?

• π/4 radians

• -π/4 radians

• π/2 radians

• -π/2 radians

What is the slope of a line with a tangent of -1?

• 0

• Undefined

• -1

• 1

Why can't the inverse tangent function map to multiple values?

• Because it would be undefined.

• Because it would not be a function.

• Because it would be a linear function.

• Because it would be a constant.

What is the valid range for the inverse tangent function?

• From -π to π

• From -π/2 to π/2

• From 0 to π

• From 0 to 2π

What happens to the tangent function at π/2 and -π/2?

• It becomes negative one.

• It becomes one.

• It becomes undefined.

• It becomes zero.

In which quadrants is the inverse tangent restricted?

• First and fourth

• Second and third

• Third and fourth

• First and second