A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function. The function has period 0.8 seconds, amplitude 6 cm, and midline H = 15 cm. At time t = 0.5 seconds, the bob is at its midline, moving towards the wall. Find the formula of the trigonometric function that models the distance H from the pendulum's bob to the wall after t seconds. Define the function using radians. H(t) =

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: Which of the following is true about sine and cosine functions?

A: It is known that the range of sine and cosine functions is [-1,1]. Thus, first statement is false.

Q: Use a sketch to find the exact value of the expression cot (sin-1 5/13)

A: So, Opposite=5, hypotenuse=13 And

Q: Use a calculator to evaluate the trigonometric function tan π/9. Round your answer to four decimal…

A:

Q: What is the range of the sine function?

A: We know, domain of sine function is all real numbers. Also, -1≤sinx≤1 ⇒range of sinx is [-1,1].

Q: Find the values of the trigonometric functions of from the information given.

A:

Q: Determine the Period of the Trigonometric Functions

A: we have to determine the period of  the trigonometric functions.

Q: With the bottom of the right triangle being 11 and the right side being 6, The bottom left corner is…

A: Given: The bottom of the right triangle being 11 and the right side being 6.  So, the figure is…

Q: Find the exact value of the expression whenever it is defined.sin (arcsin 1/2 + arccos 0)

A: Our Aim is to find the exact value of the expression given below:-sin sin-112+cos-10-(i)

Q: Determine the period of the following trigonometric function. Y = 2 sin

A: We are asked to find the period of the function.

Q: Find the remaining trigonometric functions of theta if sin theta = 1/2 and terminates it

A: Given: sinθ=12 we know that sinθ is positive in first and second quadrant if, θ is in first quadrant…

Q: A ball attached to a spring is raised 2 feet and released with an initial vertical velocity of 3…

A:

Q: Find the exact value of the remaining trigonometric functions of θ.

A: Consider the given graph tanθ=-34

Q: The largest possible value for the sine or cosine function is _______ and the smallestpossible value…

A: The largest possible value for the sine or cosine function is _______ and the smallest possible…

Q: A light block hangs at rest from the end of a spring when it is pulled down 10 cm and released.…

A: When spring is stretched and released then the block start to perform SHM with some velocity, v.…

Q: Is the sine function even, odd, or neither?

A: We know that, a function fx is said to be even if and only if f-x=fx. Also a function fx is said to…

Q: Use a middlesum with n = 4 to estimate / cos(vr + 4) dx. Make sure that your calculator is in…

A: Given fx= ∫-412cosx+4dx  and n=4

Q: A revolving beacon is situated 380 feet off a straight shore. If the beacon turns at 4.2 radians per…

A: Given revolving beacon is situated 380 feet off a straight shore and it turns at 4.2 rad per sec.…

Q: Use the figure to find the exact value of the trigonometric function. sin 2. %3D

A: To find the exact value of  From the given figure,

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

A: Given Data: The tangent of angle A is: tanA=512   The right-angle triangle ABC is shown in the…

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-foot ladder rests against a wall. If the top of the ladder starts sliding down along the wall…

A:

Q: A bicycle with 28 inch diameter wheels is moving at a steady speed. If the wheels are turning at…

A:

Q: Find the exact value

A: Given, sincos-1-23

Q: State the definition of the hyperbolic cosine and hyperbolic sine functions.

A: We define hyperbolic cosine and sine function as,

Q: State the definitions of the hyperbolic cosine and hyperbolic sine functions.

A: Given sine and cosine function.

Q: Without using a calculator, find the exact value TE of sinif cos = 3,0 ≤ 0 <

A:

Q: Write the equation of a sine function that has the following characteristic: 1 Amplitude: 4 Period:…

A: General form of a sine function is,             y=Asin(Bx-C)+D Where,      A= amplitude       Period…

Q: As theta increases from 0 0to 90 0, the value of sin theta tends toward what number?

A: The value of θ increases from  0° to 90°. The value of  sin θ is defined as; θ 0 30° 45° 60° 90°…

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: What is the equation of the sine function whose graph has an amplitude of 4, a period of TT/6, and…

A: Amplitude is 4, period is π6 and shifted π2 units to the left of t axis. Therefore,…

Q: Explain what is meant by the period of a trigonometric function.

A: The distance between the repetition of any function is called the period of the function. In…

Q: Write the equation of a sine function that has the given characteristics. Amplitude: 18 Period: 12…

A:

Q: Write the equation of a sine function given the following characteristics: Amplitude = 3, Period =…

A:

Q: Write the first trigonometric function in terms of the second for θ in the given quadrant. tan(θ),…

A: The first trigonometric function in terms of the second for θ:   Given trigonometric functions,…

Q: Find the exact value of the remaining trigonometric functions of θ. sec θ =-3,  tan θ &gt; 0

A: Given: secθ=-3, tanθ&gt;0 we know that secθ&lt;0 and  tanθ&gt;0 in third quadrant, and in third…

Q: How are the sine and cosine functions related to the other fourtrigonometric functions?

A: The objective is to show how the sine and cosine functions are related to the other four…

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: . What is the mathematical relationship between sine and cosecant, cosine and secant, and tangent…

A:

Q: Find the period of the trigonometric function g(x) = 2 sin()

A: Given data: The expression for the given function is g(x)=2sin(x/2). The standard expression for the…

Q: The value of sin7n from the unit circle is (0,1) '† (1,0) (-1,0) (0,-1)

A: Consider the unit circle given below :

Q: Find the exact circular function value for sin 3

A:

Q: Find an angle 0 with 0° < 0 < 360° that has the same: Sine function value as 220° 0 = | -0.64279 x…

A: Here we will use the trigonometric relations and properties related to all 4 quadrants to find the…

Q: Write the first trigonometric function in terms of the second for 0 in the given quadrant. cos(0),…

A: As we know that sin2x+cos2x=1 see below the answer and explanation

Q: Find the exact value of the trigonometric function at the given real number. (0) coo(-) (0) sec(-플)…

A:

Q: Use your calculator to find sec-1 8. in radians. Round your answer to four decimal places.

A:

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.