PreCalc Ch.4 Lessons 4 and 5: Trig Functions and Transformations

• 1

• 3

• 0

• 2

Answer explanation

The amplitude of a sine function is the coefficient in front of the sine term. In the function y = 3sin(x), the amplitude is 3. Therefore, the correct answer is 3.

Tags

CCSS.HSF-IF.C.7E

Answer explanation

The period of the cosine function is given by \( \frac{2\pi}{|b|} \), where \( b \) is the coefficient of \( x \). Here, \( b = 2 \), so the period is \( \frac{2\pi}{2} = \pi \). Thus, the correct answer is \( \pi \).

Tags

CCSS.HSF.TF.A.4

• Cosine graph

• Sine graph reflected over x-axis

Answer explanation

The equation y = sin(x - π/2) represents a sine graph shifted right by π/2. This is because subtracting π/2 from x moves the graph to the right along the x-axis.

Tags

CCSS.HSF-IF.C.7E

• -2

• 2

• 1

• 0

Answer explanation

The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine. Here, the coefficient is -2, so the amplitude is |-2| = 2. Thus, the correct answer is 2.

Tags

CCSS.HSF-IF.C.7E

Answer explanation

The period of the tangent function, y = tan(x), is π. This means that the function repeats its values every π units along the x-axis, making π the correct choice among the options.

Answer explanation

The amplitude of a sine function is given by the coefficient in front of the sine. Here, the correct choice is y = 4sin(x), which has an amplitude of 4. The period is 2π, matching the standard sine function.

Sri and Harshini are exploring trigonometric functions in class. Can you help them out? What is the reciprocal of the sine function?

Answer explanation

The reciprocal of the sine function is the cosecant function, denoted as \csc(x). This means \csc(x) = \frac{1}{\sin(x)}. Therefore, the correct answer is \csc(x).

Tags

CCSS.HSF.TF.A.2

• Vertical stretch by 2

• Vertical shift up by 2

• Horizontal shift right by 2

• Reflection over x-axis

Answer explanation

The transformation from \(y = \sin(x)\) to \(y = \sin(x) + 2\) involves adding 2 to the function, which shifts the graph vertically upwards by 2 units. Thus, the correct choice is 'Vertical shift up by 2'.

Tags

CCSS.HSF-IF.C.7E

Answer explanation

To solve \( \sin(x) = 0.5 \), we find the angles where sine equals 0.5 in the interval \( 0 \leq x < 2\pi \). These angles are \( x = \frac{\pi}{6} \) and \( x = \frac{5\pi}{6} \), making the correct choice \( x = \frac{\pi}{6}, \frac{5\pi}{6} \).

Tags

CCSS.HSF.TF.B.7

• Reciprocal of sine function

• Reciprocal of cosine function

• Reciprocal of tangent function

• Reciprocal of cotangent function

Answer explanation

The function y = sec(x) is defined as the reciprocal of the cosine function, which means sec(x) = 1/cos(x). Therefore, the correct answer is the reciprocal of the cosine function.