Inverse Trigonometric Functions Concepts

The video tutorial covers the tangent function, its graphing, and the concept of asymptotes. It explains the domain and range of inverse trigonometric functions, highlighting the differences between sine, cosine, and tangent. The tutorial also addresses the ambiguity in the sine rule compared to the cosine rule, particularly in dealing with obtuse angles. Finally, it discusses the boundaries of the tan inverse function and prepares students for mixing inverse trig functions with original functions.

What is the behavior of the tangent function between its asymptotes?

• It is decreasing.

• It is increasing.

• It is constant.

• It is oscillating.

When graphing tangent functions, what is the standard point used for scale?

• Pi on 2

• Pi on 4

• Pi on 6

• Pi on 3

What is the domain of the inverse sine function?

• 0 to Pi

• -1 to 1

• -Pi to Pi

• -Pi/2 to Pi/2

What is the domain of the inverse cosine function?

• -Pi/2 to Pi/2

• -Pi to Pi

• -1 to 1

• 0 to Pi

Why does the sine rule have an ambiguous case?

• Because it can only find acute angles.

• Because it is outside the domain for obtuse angles.

• Because it only works for right triangles.

• Because it cannot calculate angles.

What angle does the sine rule provide if the actual angle is obtuse?

• The obtuse angle itself

• No angle

• The equivalent acute angle

• A right angle

What is the range of the inverse tangent function?

• -1 to 1

• -Pi to Pi

• -Pi/2 to Pi/2

• 0 to Pi

Why can't the inverse tangent function reach its boundary values?

• Because they are undefined.

• Because they are asymptotes.

• Because they are zero.

• Because they are infinite.

What happens when you mix inverse trig functions with original functions?

• They cancel each other out.

• They produce a new function.

• They become undefined.

• They remain unchanged.

What is the main difference between the range of inverse sine and inverse tangent functions?

• Inverse sine includes boundaries, inverse tangent does not.

• Inverse tangent includes boundaries, inverse sine does not.

• Both include boundaries.

• Neither includes boundaries.