Math 2417 – Test #3 Review Flashcards

These flashcards cover key concepts from the Math 2417 test review, ranging from trigonometric identities to the evaluation of composite functions.

What are the inverse sine, inverse cosine, and inverse tangent functions used for?

They are used to interpret angles in circular motion.

What are the restrictions on the domain of trigonometric functions?

The domain restrictions affect how we evaluate inverse trigonometric functions.

How do you evaluate a composite function involving trigonometric and inverse trigonometric functions?

You apply the properties of both functions to simplify the expression.

What are some trigonometric identities used for?

They are used to simplify trigonometric expressions.

What formulas are used to evaluate sine and cosine functions in right triangles?

Angle sum, angle difference, double angle, and half-angle formulas.

What does the reference angle refer to?

The acute angle formed by the terminal side of the angle and the horizontal axis.

What methods can be used to solve applications involving right triangles?

Construct and analyze the right triangle using given information about trigonometric functions.

How can you solve for an oblique triangle?

You can use the law of sines or the law of cosines.

How is the area of a triangle calculated from its sides?

Using either two side lengths and the included angle or all three side lengths.

What is the purpose of converting polar coordinates to rectangular coordinates?

To graph points in a different coordinate system.

How can you calculate the magnitude of a vector?

By using the formula √(x² + y²) for its components.

What is a unit vector?

A vector with a magnitude of 1, indicating direction only.

What is the law of sines used for?

To find unknown lengths or angles in non-right triangles.

What does it mean to establish a trigonometric identity?

To show that two trigonometric expressions are equivalent for all values in their domain.

What key mathematical structures are used in polar coordinates?

The radius (r) and angle (θ) define the location in polar coordinates.

What is the significance of using right triangle trigonometry?

It helps relate the angles and sides of right triangles using trigonometric functions.

Describe the requirement for angles when applying the inverse trigonometric functions.

The angles must fall within the principal range defined for each inverse function.

What does it mean for two angles to be coterminal?

They share the same terminal side when drawn in standard position.

How do you convert rectangular coordinates to polar coordinates?

Using the formulas r = √(x² + y²) and θ = arctan(y/x).

What techniques do you need to solve trigonometric equations?

Finding all solutions requires understanding the periodic nature of trigonometric functions.

What does the graph of sin function generally look like?

It displays a wave pattern oscillating between -1 and 1.

How do you handle angles greater than 360 degrees in trigonometry?

By reducing them using modulo operation with respect to 360 degrees.

What do angle sum identities help compute?

They help compute the sine and cosine of the sum (or difference) of two angles.

How is the height of an object modeled in trigonometric functions?

Typically, it can be described by a sinusoidal function representing oscillations.