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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E