Graphing Trigonometric Function Practice

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.

Front

How do you determine the amplitude from the equation of a sine or cosine function?

Back

In the equation of the form y = A sin(Bx + C) or y = A cos(Bx + C), the amplitude is given by the absolute value of A.

Front

What is the phase shift of a trigonometric function?

Back

The phase shift is the horizontal shift left or right for periodic functions, determined by the value of C in the equation y = A sin(Bx + C) or y = A cos(Bx + C).

Front

How do you calculate the phase shift from the equation of a sine or cosine function?

Back

The phase shift is calculated as -C/B. If C is positive, the shift is to the left; if negative, the shift is to the right.

Front

What is the vertical shift in a trigonometric function?

Back

The vertical shift is the amount the graph is moved up or down, determined by the value of D in the equation y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What is the period of a trigonometric function?

Back

The period is the distance along the x-axis for one complete cycle of the function, calculated as 2π/B for sine and cosine functions.

Front

How do you find the period from the equation of a sine or cosine function?

Back

The period is found using the formula Period = 2π/|B|, where B is the coefficient of x in the function.

Front

What is the difference between sine, cosine, and tangent functions?

Back

Sine and cosine functions represent the y and x coordinates of a point on the unit circle, respectively, while tangent is the ratio of sine to cosine.

Front

What is the range of the sine and cosine functions?

Back

The range of both sine and cosine functions is [-1, 1].

Front

What is the range of the tangent function?

Back

The range of the tangent function is all real numbers (-∞, ∞).