Trigonometric Functions and Their Inverses

The video tutorial explores the graph of the cosine function and the need to restrict its domain for practical use. It highlights the ambiguous case in the sine rule when solving triangles and contrasts it with the cosine rule, which avoids such ambiguity. The tutorial also delves into inverse trigonometric functions, explaining their properties and how to remember their behavior based on the portions of the original functions they are derived from.

Why is it necessary to restrict the domain of the cosine function?

• To avoid negative values

• To make it easier to calculate

• To ensure it is a one-to-one function

• To simplify its graph

What happens if you include a turning point in the domain of a trigonometric function?

• The function becomes linear

• The function becomes constant

• The function becomes undefined

• The function becomes non-injective

What is the ambiguous case in the context of the sine rule?

• A situation where the triangle is not valid

• A case where only obtuse angles are possible

• A scenario where multiple angle solutions are possible

• A situation where no solution exists

In the ambiguous case, what is the alternative angle to the acute angle found?

• 270 degrees minus the acute angle

• 90 degrees minus the acute angle

• 180 degrees minus the acute angle

• 360 degrees minus the acute angle

How does the cosine rule avoid the ambiguous case?

• By using a different formula

• By having a domain from 0 to 180 degrees

• By restricting to positive values

• By using only acute angles

Why does the sine inverse function only provide acute angles?

• Because it is defined from -90 to 90 degrees

• Because it is restricted to positive values

• Because it is always decreasing

• Because it is always increasing

What is a key difference between sine inverse and cosine inverse functions?

• Sine inverse can only give obtuse angles

• Cosine inverse can give both acute and obtuse angles

• Sine inverse is always decreasing

• Cosine inverse is always increasing

What is the range of the cosine inverse function?

• 0 to 180 degrees

• 0 to 360 degrees

• 0 to 90 degrees

• 90 to 180 degrees

What is a helpful way to remember the behavior of sine inverse?

• It is always decreasing

• It is always increasing

• It is always zero

• It is always constant

What is a common challenge when learning inverse trigonometric functions?

• Calculating their values

• Understanding their domain restrictions

• Memorizing their formulas

• Drawing their graphs