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.

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.

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.

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.

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.

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.

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 \(\frac{2\pi}{2} = \pi\).

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.

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 \(y = a\cos(b(x - c))\).

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.