The length s of a shadow cast by a vertical gnomon (a device used to tell time) of height h when the angle of the sun above the horizon is 0 can be modeled by the equation h sin(90 - 0) sin(0) 0* < 0 s 90". (a) Verify that the expression for s is equal to h cot(0). h sin(90' - 0) sin(0) sin(0) -h cot(0)

Q: We can find some of the solutions of sin x = 0.3 graphicall by graphing y = sin x and y = Use the…

A: We can find some of the solutions of sinx=0.3 graphically by graphing y=sinx and y=0.3.

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A: In order to solve the problems of this kind we need to use linear approximation formula and then…

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

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Q: 3. Two students were playing the same game. The difference in points that each scored for the game…

A: The graph is shown below:

Q: 5. gl1) = Cot3x ら。 -- HQ) = I+ Sin x 1- Sin X

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Q: (cos 0 -sin 0) d0 7. J sin 0 8. J (1 – tan 0)² de. 9. sec2 0 tan² 0 d0.

A: 7. Given integral, ∫cos θ-sin θsin θdθ

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A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the…

Q: sin x cos" п — 1 n 2 2, | co cos"-2 x d.x Show that for cos" x dx Use this to find cos4. x dx.

A: Given, ∫cos4xdx

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Q: Sin(6x+16)=Cos(3x) Round answers to the nearest hundredth (2 decimal places). What does X = ?

A: We can find the value of x as below.

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A: i) Given that expression is sinx-3cosx.It is required to write the given expression in the form…

Q: the action of a spring can be modeled by the function y=4 cos x- cos x sin x after x seconds  Within…

A: To find the height at which spring has height of 3 feet

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Q: sin (0) cos(0) d0, cos (0) dө, u = sin(0)

A:

Q: A tangent question Verify by graphing that the graphs of y = sin x and y = x/2 have one point of…

A: The graph of the given function y=sinx and y=x2  for x&gt;0 is shown below: In the above graph, it…

Q: 9. Express tan 0 in terms of sec 0 for 0 in Quadrant II.

A: We know that, sec2θ=1+tan2θ So sec2θ=1+tan2θtan2θ=sec2θ-1tanθ=±sec2θ-1 But given that θ lie in…

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A: Given, Our cycle of normal breathing takes place every 5 seconds. y=0.6sin2π5x We have a rate of…

Q: [cos x - sin x 0] cos x 1] 5. If f(x) = | sin x 0|, show that f (a)f(b) = f(a + b).

A: f(x)=cosx-sinx0sinxcosx0001

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Q: The solution to the equation sin 2x =-sin(-x) in the interval (0, 2z) includes 0, n A. B. ,0, z 3 3…

A: We can solve the question as per the criteria and conditions given.   NOTE :: As per our guidelines…

Q: A cable hangs between two poles of equal height and 24 feet apart. Set up a coordinate system where…

A:

Q: 4. Express the function f(x) = 11 sin x +7 cos x as a function in terms of sine. Express your answer…

A: To find 11sinx+7cosx in terms of sine function only.

Q: 9. Solve the equation for x if 0 < x < 27. 2 cos x + tan x - sec x = 0 VI

A: The correct option is option A. Use the trigonometric ratios and identities to rearrange the given…

Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

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Q: cosh(2æ) – 1 Verify the identity sinh? (x) using the definitions of the hyperbolic functions.

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Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

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Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

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Q: 10. Solve the equation for x if 0 < x < 2n. 2 sin x - cot x = csC X

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Q: 1. Find the all real roots of the equation : cos(2x) - x/2 = 0, x in radians Use the Method of…

A: The given problem is to find the approximate real roots for the given function using False position…

Q: 8. A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: Let f(x) 1.9 sin(x) + 6.9 cos(x). What is the maximum and minimum value of this function? max min =…

A: Given f(x)=1.9sin(x)+6.9cos(x)

Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

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A: To evaluate the value of given integral. Use the identities: 1.sin A cos B=12sin(A+B)+sin (A-B)2.sin…

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Q: Determine the points in the interval (0, 2π) at which the graph of the function below has a…

A: Given function is, f(x) = 10 cos x + 5 sin 2 x The function has its horizontal tangent when its…

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Q: Q6 (i) Show that sin 20(tan 0+ cot0) = 2. (ii) Hence (a) find the exact value of tan+tan+cot+cot,…

A: see below the calculation and answer

Q: 3.Sinx sec a +2 Sinto Sinx(Secxt2)=0 sinx=D0 भा 2TT Seci=-ス 4Sin3x -sinx CoS X → Sinx(Sin?x -=Sin?x.…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.