Unit 1 Part II Graphing Trig Functions Flashcard

Front

What is the equation of the graph for a vertical stretch of a cosine function?

Back

The equation is of the form y = a cos(bx + c) + d, where 'a' represents the vertical stretch. For example, y = 5 cos x is a vertical stretch of the cosine function by a factor of 5.

Front

What is the period of the function y = a sin(bx)?

Back

The period is given by the formula \( \text{Period} = \frac{2\pi}{|b|} \). For example, if b = 5, the period is \( \frac{2\pi}{5} \).

Front

What is the value of \( \csc^{-1}(2) \)?

Back

The value is \( \frac{\pi}{6} \). This means that the angle whose cosecant is 2 is \( \frac{\pi}{6} \) radians.

Front

What is the value of \( \cot^{-1}(\frac{\sqrt{3}}{3}) \)?

Back

The value is \( \frac{\pi}{3} \). This means that the angle whose cotangent is \( \frac{\sqrt{3}}{3} \) is \( \frac{\pi}{3} \) radians.

Front

What is the midline of the function y = 2cos(\frac{1}{3}x + \frac{\pi}{6}) + 2?

Back

The midline is the horizontal line that passes through the average value of the function, which is +2 in this case.

Front

Define the term 'amplitude' in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline to the peak (or trough) of the graph. For example, in y = 3 sin x, the amplitude is 3.

Front

What is the effect of changing the value of 'b' in the function y = a sin(bx)?

Back

Changing 'b' affects the period of the function. The period is calculated as \( \frac{2\pi}{|b|} \). A larger 'b' results in a shorter period.

Front

What is the range of the function y = a cos(x) + d?

Back

The range is given by [d - |a|, d + |a|]. For example, for y = 2 cos(x) + 1, the range is [-1, 3].

Front

What is the phase shift of the function y = a sin(bx + c)?

Back

The phase shift is calculated as \( -\frac{c}{b} \). For example, in y = 2 sin(3x - \frac{\pi}{2}), the phase shift is \( \frac{\pi}{6} \) to the right.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. Specifically, \( \sin(x) = \cos(x - \frac{\pi}{2}) \).