Answers IC Pre-Cal - DeeringGeneral Form of Sine and Cosine

General Form of Sine and Cosine — Unit test Answers

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Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

The reference angle should be , and the sign of the value should be negative.

The reference angle should be , and the cosine value for is .

The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting in the first step.

The cosine value for is , and the reference angle and quadrant should be determined by subtracting in the first step.

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A waterwheel has a radius of 5 feet. The center of the wheel is 2 feet above the waterline. You notice a white mark at the top of the wheel. How many radians would the wheel have to rotate for the white mark to be 3 feet below the waterline?

radians

Which function is equivalent to the inverse of ?

Option

An angle that shares the same sine value of an angle that measures radians is located where?

Quadrant I

Quadrant II

Quadrant IV

along an axis

Which graph represents the function y = cos(4x)?

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 1).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 1).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at pi. It crosses the y-axis at (0, 0).

On a coordinate plane, a function has a maximum at 1 and minimum at negative 1. It completes one period at StartFraction pi Over 2 EndFraction. It crosses the y-axis at (0, 0).

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.Which function models the horizontal displacement as a function of time in seconds?

y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x)

y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x)

y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x)

y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)

On which interval are both the sine and cosine functions increasing?

(StartFraction 3 pi Over 2 EndFraction, 2 pi)

(StartFraction pi Over 2 EndFraction, pi)

(0, pi)

(pi, StartFraction 3 pi Over 2 EndFraction

Which values for have the same reference angles?

, ,

The motion of a weight that hangs from a spring is represented by the equation . It models the weight’s height, h, in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 4 inches below the rest position? Round to the nearest hundredth, if necessary.

0 seconds

0.29 seconds

0.39 seconds

1.95 seconds

Which is the graph of ?

A smooth curve resembling an arctangent function. The x-axis ranges from -6 to 6, and the y-axis from -p to p. The curve approaches horizontal asymptotes at y = p/2 and y = -p/2, passing through the origin.

A graph of a function with asymptotic behavior. The x-axis ranges from -5 to 5, and the y-axis ranges from -p to p. The curve is located in the fourth quadrant, approaching the y-axis asymptotically as x approaches zero from both positive and negative directions. The curve also approaches zero asymptotically as x moves away from zero in both directions. The function does not intersect either axis.

A graph of a function with the x-axis ranging from -2.5 to 2.5 and the y-axis ranging from -p to p. The curve passes through the origin (0,0) and changes direction at y=0. It intersects the x-axis at two points, approximately at x=-1 and x=1. The curve is symmetric about the origin.

The image shows a mathematical graph plotted on a Cartesian coordinate system. The x-axis ranges from -2 to 2, and the y-axis ranges from -p to p. A smooth, continuous curve intersects the x-axis at approximately 1. The curve extends into both the positive and negative quadrants. The point p is labeled on the positive y-axis and -p on the negative y-axis.