A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is 24 feet wide at road level and is 20 feet tall at its highest point. (a) Find an equation for the sine curve that fits the opening. Place the origin at the left end of the opening. (b) If the road is 12 feet wide with 6-foot shoulders on each side, what is the height of the tunnel at the edge of the road? 20 ft 12 ft 24 ft

Q: The top of a 15-foot ladder rests against a vertical wall with the bottom of the ladder on level…

A: The top of a 15-foot ladder rests against a vertical wall with the bottom of the ladder on level…

Q: Is the sine function even, odd, or neither? Is its graph symmetric? With respect to what?

A: To find:  If the sine function even or odd Is the graph symmetric and with respect to what.

Q: Why are trigonometric functions ideally suited to model phenomena that repeat in cycles?

A: Trigonometric functions sin, cos, tan, cosec, sec, and cot are periodic functions. That is after…

Q: Write the equation for a cosine function with amplitude 8x, period 1, and phase shift - 2.

A: The cosine function has amplitude 8π, period 1 and phase shift -2

Q: Find the exact value of the expression sin[arcsin(−0.2)], if possible.

A:

Q: How can you use the algebraic equation of a sine or cosine to find its amplitude and period- what is…

A: Given : Agebraic equation of a sine or cosine to find its amplitude and period

Q: explain why sine or cosine will never have a value greater than 1

A: To explain the given problem

Q: Write the formula forGeneral Sine Curves?

A: The formula for general sine curve is y = a sin [b(x - c)] +d

Q: Write an equation of the cosine function with amplitude 2 and period 6t.

A:

Q: 4. Determine two equations, one in terms of sine and the other in terms of cosine for the following.

A: To determine the two equations, we just have to evaluate one of them andthe other can simply be…

Q: A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start,…

A:

Q: Write the equation of a sine function that has the given characteristics. Amplitude: 3 and Period:…

A: A sine function has Amplitude: 3 and Period:π

Q: Draw the sine function in graph form

A: Given, Amplitude=2 Period = 6 π Vertical shift up=2

Q: Sketch one complete cycle of the following by first graphing the appropriate sine or cosine curve…

A: Given :- One complete cycle of the following by graphing the appropriate sine or cosine curve and…

Q: Draw graphs to show the difference in sine and cosine functions.

A: Consider the functions y=sin x  and   y=cos x. Sketch the graph of both functions as shown below.

Q: 1. A mouse wheel is 16 cm in diameter and the base of the wheel is 2 cm off the ground. If the…

A: Given: Let us consider the given data, Diameter=16 m Base=2 cm Time=14=0.25 sec Lets determine the…

Q: Find the amplitude, the period in radians, the phase shift in radians, and the vertical shift.…

A: NOTE: Refresh your page if you can't see any equations. . compare this function with  so here we…

Q: A 10-ft ladder rests against a wall at π/4 radians. If it were to begin to slip, when the bottom of…

A:

Q: Determine the equation of the cosine function that has an amplitude of 4, a period of 2T, and has a…

A: The general equation of cosine function is y=AcosBx-C+D Here,  A=AmplitudeP=2πB=PeriodCB=Horizontal…

Q: What is a periodic function? Why are the sine and cosine functions periodic?

A: Periodic function is a function which repeats its value after a regular interval. If fx+T=fx then…

Q: One period of a sine or cosine function is one ________ of the sine or cosine curve.

A: To fill in the blank in the given statement, " One period of a sine or cosine function is one…

Q: Why would a sine function be used to model the number of daylight hours?

A: We have to explain why a sine function is used to model the number of daylight hours.

Q: Use the graph of the sine to sketch one period of the graph of the function. y = −1 + 2 sin(2x…

A: It is given that, y=-1+2sin2x-π2 It is known that, if f(x) has period P, then function f(ax+b) has…

Q: Sketch the graph of the equation by making a table using values of θ that are multiples of 45°. ​…

A:

Q: A one-lane highway runs through a tunnel in the shape of one-half a sine curve cycle. The opening is…

A: The equation for sine curve that fits the opening is shown on board, where x=opening length, a=…

Q: 12. If a bicycle wheel makes 7 rotations a second and has a diameter of 75 cm, what cosine function…

A: The bicycle wheel makes 7 rotations a second and has a diameter of 75cm. Then the period of the…

Q: Find the amplitude, the period, and the phase shift and sketch the graph of the equation.

A: For any graph of the function of the form,                            y= A sinBx+C+D Here A is the…

Q: Write the equation of a sine or cosine function to describe the graph. 5- 3. 15 -- 4 2 talt 4.

A: In the given problem we have to define sine or cosine function.

Q: Write the equation of a sine function with Amplitude = 2 and Period = 8T.

A:

Q: What does the midline, period, amplitude, and horizontal shift of a graph represent in the real…

A: Amplitude is the vertical distance between the midline and one of the maximum or minimum points. We…

Q: If the sine function whose graph is the graph of TT y = -2 sin 2 (x – 4) + 1 shifted units to the…

A: Given: The graph of function y=-2sin2x-π4+1 is shifted π2 units to the left and 3 units upward, To…

Q: Determine the amplitude and period of y = - 2 sin (5x)without graphing.

A: A sinusoidal function is a function of the form A sin(Bx+C)+D. So a sinusoidal function is any…

Q: How do you use the algebraic equation of a sine or cosine to find its amplitude and period? What is…

A:

Q: What is a a sine equation for a graph with an amplitude of 6, a period of pi/3, a phase shift to the…

A:

Q: Write the equation of a sine function that has: an amplitude of 10, a period of 180 degrees, a phase…

A: The standard form of a sine function is y = asin[b(x−h)]+k  where a is the amplitude, = 10 2π/b is…

Q: On a piece of graph paper, create an amplitude vs. time graph of a sine wave with an amplitude of 5…

A: Given : 1. Create an amplitude vs. time graph of a sine wave Amplitude = 5 pa The SI unit of…

Q: One of the two acute angles in a right triangle has tangent of 5/12 . Find the sine of the other…

A: One of the two acute angles in a right triangle has tangent of 512 Let the acute angle having a…

Q: Complete the general form of the equation of a sinusoidal function having an amplitude of 4, a…

A:

Q: Choose the correct graph of the sin function from 0 to 2 ↑ if the amplitude is 1.5 and the period is…

A: We have to draw the correct graph of sin function.

Q: If the sine function whose graph is the graph of y = -2 sin 2 (x – -) + 1 shifted 4. units to the…

A: To find the equation after the transformations given

Q: How do you find the period for a sine function by looking at its graph?

A: Given,  The graph of sine function.

Q: How would I answer this Write a sine function that has an amplitude of 2, a midline of 3 and a…

A:

Q: The graph of the sine function illustrates how the ____________ of a point on the unitcircle varies…

A: Given  The graph of the sine function illustrates how the ____________ of a point on the unit circle…

Q: What does the amplitude of a sine or cosine function measure?

A: To describe what does the amplitude of a sine or cosine function measure.

Q: Write the equation of a sine function that has the following characteristics. 1 Amplitude: 5 Period:…

A:

Q: Write the equation of a negative sine equation for the graph attached.

A:

Q: If you know the sine value for a given angle, how can you quickly find the cosecant value for that…

A: See attached file for a detailed explanation and I also give an example so you can easily…

Q: Given the graph of a sine function. What is its amplitude?

A: here we have to find the amplitude of a sine function graph.

Q: In one area of the Bay of Fundy, the water has a depth of 6m at high tide, and a depth of 2m at low…

A:

Q: Sketch two cycles of a sinusoidal function that has a period of 15 seconds, an amplitude of 4 and…

A: see below the answer

Q: The height of a nail in a bicycle tire as it rotates around is periodic in nature. The radius of the…

A:

Q: Draw Graphs of the sine and cosine functions?

A: The graph of sine function is,

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.