TRIG UNIT REVIEW (Trig Graphs & Their Applications)

Front

What is the amplitude of a sine function?

Back

The amplitude is the maximum height of the wave from its midline. It is represented by the coefficient in front of the sine function.

Front

What is the period of a sine or cosine graph?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It can be calculated using the formula \( \frac{2\pi}{B} \), where B is the coefficient of x in the function.

Front

What does the equation \( y = A \sin(Bx + C) + D \) represent?

Back

This is the general form of a sine function, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

How do you find the minimum height of a wave represented by \( y = 5\sin\left(\frac{\pi}{2}x\right) + 3 \)?

Back

The minimum height occurs when \( \sin \) is at its minimum value of -1. Thus, the minimum height is \( 5(-1) + 3 = -2 \) feet.

Front

What is the vertical shift in the function \( y = 3\sin(7x) - 2 \)?

Back

The vertical shift is -2, meaning the entire graph is shifted down by 2 units.

Front

What is the effect of changing the coefficient B in the sine function \( y = A \sin(Bx) \)?

Back

Changing B affects the period of the wave. A larger B results in a shorter period.

Front

What is the equation for a sine function with an amplitude of 6 and a period of \( \frac{\pi}{4} \)?

Back

The equation is \( y = 6\sin(8x) \). The period is calculated as \( \frac{2\pi}{B} = \frac{\pi}{4} \), so B = 8.

Front

What is the maximum height of the wave represented by \( y = 5\sin\left(\frac{\pi}{2}x\right) + 3 \)?

Back

The maximum height occurs when \( \sin \) is at its maximum value of 1. Thus, the maximum height is \( 5(1) + 3 = 8 \) feet.

Front

What is the phase shift of the function \( y = 2\sin(3x - \frac{\pi}{2}) \)?

Back

The phase shift can be found by setting \( 3x - \frac{\pi}{2} = 0 \), which gives a phase shift of \( \frac{\pi}{6} \) to the right.

Front

How do you determine the amplitude from the equation \( y = -2\sin(4x) + 1 \)?

Back

The amplitude is the absolute value of the coefficient in front of the sine function, which is 2.