Simplifying Rational Expressions Answers
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?
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.
Which is the graph of ?
A student is given that point P(a, b) lies on the terminal ray of angle , which is between radians and 2 radians. The student uses the steps below to find cos . Step 1Find the quadrant in which P(a, b) lies:P(a, b) is in Quadrant IV.Step 2Use the point and the Pythagorean theorem to determine the value of r:, but since r must be positive, .Step 3Determine cos ., where a and b are positive.Which of the following explains whether the student is correct?
The graph of which function passes through (0,3) and has an amplitude of 3?
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?
Which statement is true about the graph of the equation ?
If a vertical line is dropped from the x-axis to the point (12, –9) in the diagram below, what is the value of sec ?
An angle in standard position measures radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle?
Which values for have the same reference angles?
Which of the following is true for f(x) = –2sin(x) – 3?
Which statement is true about the graph of the equation ?
Which formula gives the zeros of y = sin(x)?
An angle that shares the same sine value of an angle that measures radians is located where?
The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation , where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. Which equation also models this situation?
The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . What is the height of the ball at its equilibrium?
Which statement accurately describes how adding a number, n, to the function affects its graph?
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.
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