ALB M3 Trig Test Review

Front

What is the vertical shift in a trigonometric function?

Back

The vertical shift refers to the amount by which the graph of a function is moved up or down on the coordinate plane. For example, a vertical shift of 'Down 4' means the entire graph is moved 4 units down.

Tags

CCSS.HSF-IF.C.7E

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by \(\frac{180}{\pi}\). For example, to convert \(\frac{7\pi}{4}\) radians to degrees, calculate \(\frac{7\pi}{4} \times \frac{180}{\pi} = 315\) degrees.

Tags

CCSS.HSF.TF.A.1

Front

What is the radian equivalent of 150 degrees?

Back

To convert 150 degrees to radians, use the formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\). Thus, \(150 \times \frac{\pi}{180} = \frac{5\pi}{6}\) radians.

Tags

CCSS.HSF.TF.A.1

Front

What is the value of \(\cos(225^{\circ})\)?

Back

The value of \(\cos(225^{\circ})\) is \(-\frac{\sqrt{2}}{2}\). This is because 225 degrees is in the third quadrant where cosine values are negative.

Tags

CCSS.HSF.TF.A.2

Front

What does the equation \(y = -4\sin x + 2\) represent?

Back

This equation represents a sine wave that has been vertically shifted up by 2 units and reflected over the x-axis, with an amplitude of 4.

Tags

CCSS.HSF-IF.C.7E

Front

What is the amplitude of a sine function?

Back

The amplitude of a sine function is the maximum distance from the midline of the graph to its peak. It is determined by the coefficient in front of the sine function.

Tags

CCSS.HSF-IF.C.7E

Front

How do you find the period of a sine function?

Back

The period of a sine function \(y = a\sin(bx)\) is given by the formula \(\frac{2\pi}{|b|}\). For example, if \(b = 2\), the period is \(\frac{2\pi}{2} = \pi\).

Tags

CCSS.HSF.TF.A.4

Front

What is the range of the function \(y = 3\cos x\)?

Back

The range of the function \(y = 3\cos x\) is from -3 to 3, as the cosine function oscillates between -1 and 1, and is scaled by a factor of 3.

Tags

CCSS.HSF-IF.C.7E

Front

What is the phase shift in a trigonometric function?

Back

The phase shift is the horizontal shift left or right for periodic functions. It is determined by the value of \(c\) in the equation \(y = a\sin(b(x - c))\) or \(y = a\cos(b(x - c))\).

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the vertical shift of a trigonometric function?

Back

The vertical shift is determined by the constant added or subtracted from the function. In \(y = a\sin x + d\), the value of \(d\) indicates the vertical shift.

Tags

CCSS.HSF-IF.C.7E