Pre-Calculus REVIEWER 2

What does the amplitude of a trigonometric function represent?

• The vertical shift of the graph

• The horizontal shift of the graph

• The maximum absolute value of the function's output

• The number of cycles completed in one period

Answer explanation

The amplitude of a trigonometric function represents the maximum distance from the function's midline to its peak or trough, indicating the height or intensity of its oscillation.

In the function y = 3sin(2x - π/4), what is the amplitude?

• 2

• 3

• -3

• π/4

Answer explanation

The amplitude of the function y = 3sin(2x - π/4) is 3.

Which of the following represents the period of the function y = 4cos(3x)?

• 4

• 3

• 2π/3

• 2π/3

Answer explanation

The period of the function y = 4cos(3x) is given by 2π divided by the coefficient of x, which is 3, resulting in a period of 2π/3.

For the function y = -2cos(x + π/2), what is the phase shift?

• π/2 units to the left

• π/2 units to the right

• No phase shifts

• 2π units to the left

Answer explanation

The function y = -2cos(x + π/2) has a phase shift of π/2 units to the right, as the argument inside the cosine function is adjusted by adding π/2.

What is the range of the function y = 5 + 3sin(x)?

• [2, 8]

• [3, 8]

• [-2, 8]

• [3, 5]

Answer explanation

The range of the function y = 5 + 3sin(x) can be obtained by considering that the sine function oscillates between -1 and 1; adding 5 and multiplying by 3 extends the range to [2, 8].

A Ferris wheel completes a full revolution every 60 seconds. The height of a passenger can be modeled by the function h(t) = 30sin(π/30 * t) + 40, where h(t) represents the height in feet above the ground and t represents time in seconds. What is the amplitude of this function?

• 30 feet

• 40 feet

• 10 feet

• 70 feet

Answer explanation

Which of the following statements is true about trigonometric identities?

• They are true for specific values of the variables.

• They are true for all values of the variables within the domain.

• They have limitations in their validity.

• They are only true for integers.

Answer explanation

Trigonometric identities are true for all values of the variables within their specified domains, providing universally valid relationships among trigonometric functions.

Determine if the equation sinx2(x) + cosx2(x) = 1 is an identity or a conditional equation.

• Identity

• Conditional equation

• Neither

• Both

Answer explanation

Which of the following equations is an identity?

• tan(x) = sin(x)cos(x)

• sin(x) + cos(x) = cos(x)

• cot(x) = 1tan(x)

• sin(2x) = 2sin(x) cos(x)

Answer explanation

Determine if the equation tan(x) - sin(x)/cos(x)= sec(x) is an identity or a conditional equation.

• Identity

• Conditional equation

• Neither

• Both

Answer explanation