Precalculus Chapter 4 Practice Exam

Front

What is the definition of a quadrant in the Cartesian coordinate system?

Back

A quadrant is one of the four sections of the Cartesian plane, defined by the x and y axes. Quadrant I is where both x and y are positive, Quadrant II is where x is negative and y is positive, Quadrant III is where both x and y are negative, and Quadrant IV is where x is positive and y is negative.

Front

What are the coordinates of a point in Quadrant III?

Back

In Quadrant III, both the x and y coordinates are negative.

Front

What is the significance of the midline in a trigonometric graph?

Back

The midline is the horizontal line that runs through the middle of the graph, representing the average value of the function over one period.

Front

How do you determine the maximum value of a trigonometric function?

Back

The maximum value of a trigonometric function occurs at the peak of its graph, which can be found by analyzing the amplitude and midline.

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the distance from the midline to the maximum (or minimum) value of the function.

Front

How do you find the period of a sine or cosine function?

Back

The period of a sine or cosine function is calculated as 2π divided by the coefficient of x in the function's argument.

Front

What is the formula for the sine function?

Back

The sine function is defined as sin(x) = opposite/hypotenuse in a right triangle.

Front

What is the formula for the cosine function?

Back

The cosine function is defined as cos(x) = adjacent/hypotenuse in a right triangle.

Front

What is the relationship between sine and cosine in a right triangle?

Back

In a right triangle, sine and cosine are related through the Pythagorean identity: sin²(x) + cos²(x) = 1.

Front

What does it mean for a function to be periodic?

Back

A function is periodic if it repeats its values at regular intervals, known as the period.