Untitled Quiz

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Questions and Answers

What is the amplitude of the sine and cosine functions given their peaks and troughs?

1 (correct)
2
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0

What is the period of the tangent function?

720
90
180 (correct)
360

How does the cosecant function relate to the sine function?

csc θ = sin(θ) + 1
csc θ = 1/sin(θ) (correct)
csc θ = 2sin(θ)
csc θ = sin(θ/2)

What indicates a phase shift in a trigonometric function?

A horizontal movement of the function (B) Signup and view all the answers

What value defines the asymptotes for the base tangent function?

$x = 90 + 180n$ where $n ∈ ℤ$ (D) Signup and view all the answers

What is the peak value of the secant function?

Greater than or equal to 1 (D) Signup and view all the answers

For sine and cosine functions, what is the relationship between their periods?

They have the same period of 360 (D) Signup and view all the answers

How does shifting a sine function to the left affect its phase shift?

It increases the phase shift (B) Signup and view all the answers

How would you determine the amplitude of a sinusoidal function given by the equation $y = 3 \sin(2\theta) + 1$?

3 (A) Signup and view all the answers

What is the period of the function $y = \cos(5\theta)$?

$\frac{2\pi}{5}$ (C) Signup and view all the answers

Which of the following statements accurately describes the relationship between sine and cosine functions?

Sine is the cosine of the complementary angle. (D) Signup and view all the answers

Given the function $f(\theta) = -2\sin(\theta + \frac{\pi}{3})$, what is the phase shift?

$\frac{\pi}{3}$ to the left (D) Signup and view all the answers

How can you describe the effect of the negative sign in front of the sine function in the equation $y = -\sin(\theta)$?

It reflects the graph across the x-axis. (B) Signup and view all the answers

What is the domain of the function $y = \tan(\theta)$?

$\theta \neq \frac{\pi}{2} + k\pi$ for any integer k (C) Signup and view all the answers

Which transformation correctly describes the function $y = \sin(\theta) + 2$?

Vertical shift upwards by 2 units (C) Signup and view all the answers

If the function $y = 4\cos(3\theta)$ is graphed, what is the maximum value attained by the function?

4 (A) Signup and view all the answers

How is the amplitude of a sine or cosine function determined?

It is half the distance between the maximum and minimum values. (C) Signup and view all the answers

What is the period of the base sine and cosine functions?

360 degrees (B) Signup and view all the answers

In relation to each other, how can sine and cosine functions be defined?

One can be derived from the transformation of the other. (B) Signup and view all the answers

What does a phase shift in trigonometric functions represent?

A horizontal shift of the graph along the x-axis. (C) Signup and view all the answers

What will the graph of a negative sine function look like compared to its positive counterpart?

It will be reflected over the x-axis. (D) Signup and view all the answers

In the context of trigonometric functions, what does the term 'cycle' refer to?

One complete pattern of repeating behavior in the graph. (B) Signup and view all the answers

Which statement is true regarding the range of sinusoidal functions?

Their range extends from negative infinity to positive infinity. (D) Signup and view all the answers

What is the effect of shifting a trigonometric function upward by a constant value?

It translates the graph vertically but does not affect its shape. (B) Signup and view all the answers

Flashcards

Equation of axis (sine/cosine)

The horizontal line that a trigonometric function oscillates around.

Phase shift (sine/cosine)

The horizontal displacement of a trigonometric function compared to the standard sine or cosine function.