Trigonometric Functions and Their Properties

The video tutorial explores the properties of the cosine function, including its inverse, and compares the sine and cosine rules for solving triangles. It highlights the advantages of the cosine rule and discusses issues with inverse trigonometric functions. The tutorial also covers graphing trigonometric functions, emphasizing the importance of understanding their domains and asymptotes.

What is the domain of the cosine function that allows it to have an inverse?

• -2π to 2π

• 0 to π

• 0 to 2π

• -π to π

Which rule is used to solve triangles that do not have right angles?

• Tangent Rule

• Cosine Rule

• Sine Rule

• Pythagorean Theorem

What can be found using the sine or cosine rule in a triangle?

• Perimeter of the triangle

• Volume of the triangle

• Length of a side or an angle

• Area of the triangle

Why is the cosine rule considered superior in certain contexts?

• It applies to all types of triangles

• It avoids ambiguous cases

• It requires fewer calculations

• It is easier to memorize

What problem can arise when using the sine rule?

• Incorrect volume calculation

• Incorrect angle measurement

• Incorrect side length

• Incorrect area calculation

What is a common mistake when learning trigonometric rules without visualization?

• Swapping the rules

• Overcomplicating the problems

• Forgetting the formulas

• Misunderstanding the concepts

What is the gradient of tan(x) at the origin?

• Undefined

• -1

• 1

• 0

What is the significance of asymptotes in the tangent function?

• They indicate undefined points

• They define the range

• They determine the period

• They show maximum values

How many turning points does the tangent function have?

• Infinite

• Two

• None

• One

What should be done to accurately draw inverse trigonometric functions?

• Memorize the formulas

• Estimate the values

• Reflect and rotate the graph

• Use a calculator